SET007 Axioms: SET007+552.ax


%------------------------------------------------------------------------------
% File     : SET007+552 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : The For (going up) Macro Instruction
% 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    : sfmastr3 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   65 (   1 unit)
%            Number of atoms       :  604 (  78 equality)
%            Maximal formula depth :   20 (  12 average)
%            Number of connectives :  589 (  50 ~  ;  14  |; 243  &)
%                                         (   6 <=>; 276 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   39 (   1 propositional; 0-5 arity)
%            Number of functors    :   72 (  11 constant; 0-6 arity)
%            Number of variables   :  267 (   0 singleton; 265 !;   2 ?)
%            Maximal term depth    :    9 (   2 average)
% SPC      : 

% Comments : The individual reference can be found in [Mat90] by looking for
%            the name provided by [Urb08].
%          : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
%          : These set theory axioms are used in encodings of problems in
%            various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(fc1_sfmastr3,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_finset_1(A)
        & v5_membered(A) )
     => ( v1_xreal_0(k3_seq_4(A))
        & v1_int_1(k3_seq_4(A))
        & v1_xcmplx_0(k3_seq_4(A)) ) ) )).

fof(fc2_sfmastr3,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_sf_mastr(A)
        & m1_scmfsa_2(A)
        & m1_scmfsa_2(B)
        & 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)
        & 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) )
     => ( v1_relat_1(k5_scmfsa8b(A,B,C,D))
        & v1_funct_1(k5_scmfsa8b(A,B,C,D))
        & v1_finset_1(k5_scmfsa8b(A,B,C,D))
        & v1_ami_3(k5_scmfsa8b(A,B,C,D),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & v1_scmfsa_4(k5_scmfsa8b(A,B,C,D))
        & v1_scmfsa7b(k5_scmfsa8b(A,B,C,D)) ) ) )).

fof(fc3_sfmastr3,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_sf_mastr(A)
        & m1_scmfsa_2(A)
        & m1_scmfsa_2(B)
        & m1_scmfsa_2(C)
        & 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) )
     => ( v1_relat_1(k3_sfmastr3(A,B,C,D))
        & v1_funct_1(k3_sfmastr3(A,B,C,D))
        & v1_finset_1(k3_sfmastr3(A,B,C,D))
        & v1_ami_3(k3_sfmastr3(A,B,C,D),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & v1_scmfsa_4(k3_sfmastr3(A,B,C,D))
        & v1_scmfsa7b(k3_sfmastr3(A,B,C,D)) ) ) )).

fof(fc4_sfmastr3,axiom,(
    ! [A,B,C,D] :
      ( ( m1_scmfsa_2(A)
        & m1_scmfsa_2(B)
        & ~ v1_sf_mastr(C)
        & m1_scmfsa_2(C)
        & m2_scmfsa_2(D) )
     => ( v1_relat_1(k4_sfmastr3(A,B,C,D))
        & v1_funct_1(k4_sfmastr3(A,B,C,D))
        & v1_finset_1(k4_sfmastr3(A,B,C,D))
        & v1_ami_3(k4_sfmastr3(A,B,C,D),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & v1_scmfsa_4(k4_sfmastr3(A,B,C,D))
        & v1_scmfsa7b(k4_sfmastr3(A,B,C,D)) ) ) )).

fof(fc5_sfmastr3,axiom,(
    ! [A,B,C] :
      ( ( m2_scmfsa_2(A)
        & m1_scmfsa_2(B)
        & m1_scmfsa_2(C) )
     => ( v1_relat_1(k5_sfmastr3(A,B,C))
        & v1_funct_1(k5_sfmastr3(A,B,C))
        & ~ v1_xboole_0(k5_sfmastr3(A,B,C))
        & v1_finset_1(k5_sfmastr3(A,B,C))
        & v1_ami_3(k5_sfmastr3(A,B,C),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & v1_scmfsa_4(k5_sfmastr3(A,B,C))
        & v1_scmfsa7b(k5_sfmastr3(A,B,C))
        & v1_scmfsa6b(k5_sfmastr3(A,B,C))
        & v2_scmfsa6b(k5_sfmastr3(A,B,C))
        & v3_scmfsa6b(k5_sfmastr3(A,B,C)) ) ) )).

fof(t1_sfmastr3,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,A,A)
        & v3_funct_2(B,A,A)
        & m2_relset_1(B,A,A) )
     => ! [C] :
          ( m1_subset_1(C,A)
         => ! [D] :
              ( m1_subset_1(D,A)
             => ( v1_funct_1(k2_funct_7(k2_funct_7(B,C,k1_funct_1(B,D)),D,k1_funct_1(B,C)))
                & v1_funct_2(k2_funct_7(k2_funct_7(B,C,k1_funct_1(B,D)),D,k1_funct_1(B,C)),A,A)
                & v3_funct_2(k2_funct_7(k2_funct_7(B,C,k1_funct_1(B,D)),D,k1_funct_1(B,C)),A,A)
                & m2_relset_1(k2_funct_7(k2_funct_7(B,C,k1_funct_1(B,D)),D,k1_funct_1(B,C)),A,A) ) ) ) ) )).

fof(t2_sfmastr3,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B,C] :
          ~ ( r2_hidden(B,k1_relat_1(A))
            & r2_hidden(C,k1_relat_1(A))
            & ! [D] :
                ( ( v1_funct_1(D)
                  & v1_funct_2(D,k1_relat_1(A),k1_relat_1(A))
                  & v3_funct_2(D,k1_relat_1(A),k1_relat_1(A))
                  & m2_relset_1(D,k1_relat_1(A),k1_relat_1(A)) )
               => k2_funct_7(k2_funct_7(A,B,k1_funct_1(A,C)),C,k1_funct_1(A,B)) != k5_relat_1(D,A) ) ) ) )).

fof(d1_sfmastr3,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_finset_1(A)
        & v2_membered(A) )
     => ! [B] :
          ( v1_xreal_0(B)
         => ( B = k3_seq_4(A)
          <=> ( r2_hidden(B,A)
              & ! [C] :
                  ( v1_xreal_0(C)
                 => ( r2_hidden(C,A)
                   => r1_xreal_0(B,C) ) ) ) ) ) ) )).

fof(d2_sfmastr3,axiom,(
    $true )).

fof(d3_sfmastr3,axiom,(
    ! [A] :
      ( m2_finseq_1(A,k4_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( ( r1_xreal_0(np__1,B)
                  & r1_xreal_0(B,C)
                  & r1_xreal_0(C,k3_finseq_1(A)) )
               => ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ( D = k1_sfmastr3(A,B,C)
                    <=> ? [E] :
                          ( ~ v1_xboole_0(E)
                          & v1_finset_1(E)
                          & m1_subset_1(E,k1_zfmisc_1(k4_numbers))
                          & E = k2_relat_1(k2_graph_2(k4_numbers,A,B,C))
                          & k1_nat_1(D,np__1) = k1_nat_1(k5_finseq_4(k2_graph_2(k4_numbers,A,B,C),k3_seq_4(E)),B) ) ) ) ) ) ) ) )).

fof(t3_sfmastr3,axiom,(
    ! [A] :
      ( m2_finseq_1(A,k4_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ( ( r1_xreal_0(np__1,B)
                      & r1_xreal_0(B,C)
                      & r1_xreal_0(C,k3_finseq_1(A)) )
                   => ( D = k1_sfmastr3(A,B,C)
                    <=> ( r1_xreal_0(B,D)
                        & r1_xreal_0(D,C)
                        & ! [E] :
                            ( m2_subset_1(E,k1_numbers,k5_numbers)
                           => ( ( r1_xreal_0(B,E)
                                & r1_xreal_0(E,C) )
                             => r1_xreal_0(k1_funct_1(A,D),k1_funct_1(A,E)) ) )
                        & ! [E] :
                            ( m2_subset_1(E,k1_numbers,k5_numbers)
                           => ~ ( r1_xreal_0(B,E)
                                & ~ r1_xreal_0(D,E)
                                & r1_xreal_0(k1_funct_1(A,E),k1_funct_1(A,D)) ) ) ) ) ) ) ) ) ) )).

fof(t4_sfmastr3,axiom,(
    ! [A] :
      ( m2_finseq_1(A,k4_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( ( r1_xreal_0(np__1,B)
              & r1_xreal_0(B,k3_finseq_1(A)) )
           => k1_sfmastr3(A,B,B) = B ) ) ) )).

fof(d4_sfmastr3,axiom,(
    ! [A] :
      ( m2_finseq_1(A,k4_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( r1_sfmastr3(A,B,C)
              <=> ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ! [E] :
                        ( m2_subset_1(E,k1_numbers,k5_numbers)
                       => ( ( r1_xreal_0(B,D)
                            & r1_xreal_0(D,E)
                            & r1_xreal_0(E,C) )
                         => r1_xreal_0(k1_funct_1(A,D),k1_funct_1(A,E)) ) ) ) ) ) ) ) )).

fof(d5_sfmastr3,axiom,(
    ! [A] :
      ( m2_finseq_1(A,k4_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( r2_sfmastr3(A,B)
          <=> ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ( ( r1_xreal_0(np__1,C)
                        & r1_xreal_0(C,B)
                        & r1_xreal_0(D,k3_finseq_1(A)) )
                     => ( r1_xreal_0(D,B)
                        | r1_xreal_0(k1_funct_1(A,C),k1_funct_1(A,D)) ) ) ) ) ) ) ) )).

fof(t5_sfmastr3,axiom,(
    ! [A] :
      ( m2_finseq_1(A,k4_numbers)
     => ! [B] :
          ( m2_finseq_1(B,k4_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ( ( r1_xreal_0(k1_nat_1(C,np__1),k3_finseq_1(A))
                      & D = k1_sfmastr3(A,k1_nat_1(C,np__1),k3_finseq_1(A))
                      & r2_sfmastr3(A,C)
                      & r1_sfmastr3(A,np__1,C)
                      & B = k2_funct_7(k2_funct_7(A,k1_nat_1(C,np__1),k1_funct_1(A,D)),D,k1_funct_1(A,k1_nat_1(C,np__1))) )
                   => r1_sfmastr3(B,np__1,k1_nat_1(C,np__1)) ) ) ) ) ) )).

fof(t6_sfmastr3,axiom,(
    ! [A] :
      ( m2_finseq_1(A,k4_numbers)
     => ! [B] :
          ( m2_finseq_1(B,k4_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ( ( r1_xreal_0(k1_nat_1(C,np__1),k3_finseq_1(A))
                      & D = k1_sfmastr3(A,k1_nat_1(C,np__1),k3_finseq_1(A))
                      & r2_sfmastr3(A,C)
                      & B = k2_funct_7(k2_funct_7(A,k1_nat_1(C,np__1),k1_funct_1(A,D)),D,k1_funct_1(A,k1_nat_1(C,np__1))) )
                   => r2_sfmastr3(B,k1_nat_1(C,np__1)) ) ) ) ) ) )).

fof(t7_sfmastr3,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_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,k1_scmfsa6c(A))
                  & r6_scmfsa7b(C,k1_scmfsa6c(A))
                  & r4_scmfsa7b(C,B) )
               => k20_scmfsa_2(k3_scmfsa6b(C,A),B) = k20_scmfsa_2(k1_scmfsa6c(A),B) ) ) ) ) )).

fof(t8_sfmastr3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(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(k3_scmfsa6b(k5_scmfsa_4,A),k4_subset_1(u1_struct_0(k1_scmfsa_2),k2_scmfsa_2,k3_scmfsa_2)) = k7_relat_1(A,k4_subset_1(u1_struct_0(k1_scmfsa_2),k2_scmfsa_2,k3_scmfsa_2)) ) ) )).

fof(t9_sfmastr3,axiom,(
    ! [A] :
      ( m1_scmfsa_2(A)
     => r2_scmfsa7b(k5_scmfsa_4,A) ) )).

fof(t10_sfmastr3,axiom,(
    ! [A] :
      ( m1_scmfsa_2(A)
     => ! [B] :
          ( m1_scmfsa_2(B)
         => ! [C] :
              ( m1_scmfsa_2(C)
             => ( A != B
               => r1_scmfsa7b(k8_scmfsa_2(C,B),A) ) ) ) ) )).

fof(t11_sfmastr3,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] :
              ( m1_scmfsa_2(C)
             => ! [D] :
                  ( m2_scmfsa_2(D)
                 => k20_scmfsa_2(k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k16_scmfsa_2(B,C,D),A),B) = k4_finseq_4(k5_numbers,k4_numbers,k21_scmfsa_2(A,D),k1_int_2(k20_scmfsa_2(A,C))) ) ) ) ) )).

fof(t12_sfmastr3,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_scmfsa_2(B)
         => ! [C] :
              ( m1_scmfsa_2(C)
             => ! [D] :
                  ( m2_scmfsa_2(D)
                 => k21_scmfsa_2(k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k17_scmfsa_2(C,B,D),A),D) = k2_funct_7(k21_scmfsa_2(A,D),k1_int_2(k20_scmfsa_2(A,B)),k20_scmfsa_2(A,C)) ) ) ) ) )).

fof(t13_sfmastr3,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)
                & v1_scmfsa_4(C)
                & m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
             => ! [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) )
                 => k2_sf_mastr(k5_scmfsa8b(A,B,C,D)) = k4_subset_1(k2_scmfsa_2,k4_subset_1(k2_scmfsa_2,k2_sfmastr1(A,B),k2_sf_mastr(C)),k2_sf_mastr(D)) ) ) ) ) )).

fof(t14_sfmastr3,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)
                & v1_scmfsa_4(C)
                & m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
             => ( r4_scmfsa7b(C,A)
               => r4_scmfsa7b(k2_scmfsa_9(B,C),A) ) ) ) ) )).

fof(t15_sfmastr3,axiom,(
    ! [A] :
      ( m1_scmfsa_2(A)
     => ! [B] :
          ( m1_scmfsa_2(B)
         => ! [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) )
                 => ! [E] :
                      ( ( v1_ami_3(E,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
                        & v1_scmfsa_4(E)
                        & m1_ami_1(E,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
                     => ( ( r4_scmfsa7b(D,A)
                          & r4_scmfsa7b(E,A) )
                       => ( A = B
                          | r4_scmfsa7b(k5_scmfsa8b(B,C,D,E),A) ) ) ) ) ) ) ) )).

fof(d6_sfmastr3,axiom,(
    ! [A] :
      ( m1_scmfsa_2(A)
     => ! [B] :
          ( m1_scmfsa_2(B)
         => ! [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) )
                 => ! [E] :
                      ( m1_subset_1(E,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
                     => k2_sfmastr3(A,B,C,D,E) = k5_scmfsa_9(k2_scmfsa6b(k2_scmfsa6b(E,k6_sfmastr1(np__1,k4_subset_1(k2_scmfsa_2,k3_sfmastr1(A,B,C),k2_sf_mastr(D))),k2_xcmplx_0(k6_xcmplx_0(k20_scmfsa_2(E,C),k20_scmfsa_2(E,B)),np__1)),A,k20_scmfsa_2(E,B)),k6_scmfsa6a(k6_scmfsa6a(D,k9_scmfsa_2(A,k4_scmfsa_2(np__0))),k10_scmfsa_2(k6_sfmastr1(np__1,k4_subset_1(k2_scmfsa_2,k3_sfmastr1(A,B,C),k2_sf_mastr(D))),k4_scmfsa_2(np__0))),k6_sfmastr1(np__1,k4_subset_1(k2_scmfsa_2,k3_sfmastr1(A,B,C),k2_sf_mastr(D)))) ) ) ) ) ) )).

fof(t16_sfmastr3,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] :
              ( m1_scmfsa_2(C)
             => ! [D] :
                  ( m1_scmfsa_2(D)
                 => ! [E] :
                      ( ( v1_ami_3(E,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
                        & v1_scmfsa_4(E)
                        & m1_ami_1(E,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(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr3(B,C,D,E,A),np__0),k4_scmfsa_2(np__0)) = np__1 ) ) ) ) ) ) )).

fof(t17_sfmastr3,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] :
              ( m1_scmfsa_2(C)
             => ! [D] :
                  ( m1_scmfsa_2(D)
                 => ! [E] :
                      ( ( v1_ami_3(E,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
                        & v1_scmfsa_4(E)
                        & m1_ami_1(E,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
                     => k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr3(B,C,D,E,A),np__0),B) = k20_scmfsa_2(A,C) ) ) ) ) ) )).

fof(t18_sfmastr3,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] :
              ( m1_scmfsa_2(C)
             => ! [D] :
                  ( m1_scmfsa_2(D)
                 => ! [E] :
                      ( ( v1_ami_3(E,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
                        & v1_scmfsa_4(E)
                        & m1_ami_1(E,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
                     => ( B != C
                       => k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr3(B,C,D,E,A),np__0),C) = k20_scmfsa_2(A,C) ) ) ) ) ) ) )).

fof(t19_sfmastr3,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] :
              ( m1_scmfsa_2(C)
             => ! [D] :
                  ( m1_scmfsa_2(D)
                 => ! [E] :
                      ( ( v1_ami_3(E,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
                        & v1_scmfsa_4(E)
                        & m1_ami_1(E,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
                     => ( B != C
                       => k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr3(B,D,C,E,A),np__0),C) = k20_scmfsa_2(A,C) ) ) ) ) ) ) )).

fof(t20_sfmastr3,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] :
              ( m1_scmfsa_2(C)
             => ! [D] :
                  ( m1_scmfsa_2(D)
                 => ! [E] :
                      ( m1_scmfsa_2(E)
                     => ! [F] :
                          ( ( v1_ami_3(F,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
                            & v1_scmfsa_4(F)
                            & m1_ami_1(F,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
                         => ( r2_hidden(C,k2_sf_mastr(F))
                           => ( B = C
                              | k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr3(B,D,E,F,A),np__0),C) = k20_scmfsa_2(A,C) ) ) ) ) ) ) ) ) )).

fof(t21_sfmastr3,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] :
              ( m1_scmfsa_2(C)
             => ! [D] :
                  ( m1_scmfsa_2(D)
                 => ! [E] :
                      ( m2_scmfsa_2(E)
                     => ! [F] :
                          ( ( v1_ami_3(F,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
                            & v1_scmfsa_4(F)
                            & m1_ami_1(F,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
                         => k21_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr3(B,C,D,F,A),np__0),E) = k21_scmfsa_2(A,E) ) ) ) ) ) ) )).

fof(t22_sfmastr3,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] :
              ( m1_scmfsa_2(C)
             => ! [D] :
                  ( m1_scmfsa_2(D)
                 => ! [E] :
                      ( ( v1_ami_3(E,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
                        & v1_scmfsa_4(E)
                        & m1_ami_1(E,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
                     => ( k20_scmfsa_2(A,k4_scmfsa_2(np__0)) = np__1
                       => ! [F] :
                            ( ( ~ v1_sf_mastr(F)
                              & m1_scmfsa_2(F) )
                           => ( F = k6_sfmastr1(np__1,k4_subset_1(k2_scmfsa_2,k3_sfmastr1(B,C,D),k2_sf_mastr(E)))
                             => k7_relat_1(k3_scmfsa6b(k6_scmfsa6a(k6_scmfsa6a(k7_scmfsa6a(k8_scmfsa_2(F,D),k10_scmfsa_2(F,C)),k9_scmfsa_2(F,k4_scmfsa_2(np__0))),k8_scmfsa_2(B,C)),A),k4_subset_1(u1_struct_0(k1_scmfsa_2),k2_scmfsa_2,k3_scmfsa_2)) = k7_relat_1(k2_scmfsa6b(k2_scmfsa6b(A,F,k2_xcmplx_0(k6_xcmplx_0(k20_scmfsa_2(A,D),k20_scmfsa_2(A,C)),np__1)),B,k20_scmfsa_2(A,C)),k4_subset_1(u1_struct_0(k1_scmfsa_2),k2_scmfsa_2,k3_scmfsa_2)) ) ) ) ) ) ) ) ) )).

fof(d7_sfmastr3,axiom,(
    ! [A] :
      ( m1_scmfsa_2(A)
     => ! [B] :
          ( m1_scmfsa_2(B)
         => ! [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) )
                 => ! [E] :
                      ( m1_subset_1(E,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
                     => ( r3_sfmastr3(A,B,C,D,E)
                      <=> ! [F] :
                            ( m2_subset_1(F,k1_numbers,k5_numbers)
                           => ( ~ r1_xreal_0(k2_xcmplx_0(k6_xcmplx_0(k20_scmfsa_2(E,C),k20_scmfsa_2(E,B)),np__1),F)
                             => ( r5_scmfsa7b(D,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr3(A,B,C,D,E),F))
                                & r6_scmfsa7b(D,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr3(A,B,C,D,E),F)) ) ) ) ) ) ) ) ) ) )).

fof(t23_sfmastr3,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_scmfsa_2(B)
         => ! [C] :
              ( m1_scmfsa_2(C)
             => ! [D] :
                  ( m1_scmfsa_2(D)
                 => ! [E] :
                      ( ( v1_ami_3(E,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
                        & v1_scmfsa_4(E)
                        & v2_scmfsa6b(E)
                        & m1_ami_1(E,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
                     => r3_sfmastr3(B,C,D,E,A) ) ) ) ) ) )).

fof(t24_sfmastr3,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] :
              ( m1_scmfsa_2(C)
             => ! [D] :
                  ( m1_scmfsa_2(D)
                 => ! [E] :
                      ( ( v1_ami_3(E,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
                        & v1_scmfsa_4(E)
                        & v1_scmfsa7b(E)
                        & m1_ami_1(E,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
                     => ! [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,k2_sfmastr3(B,C,D,E,A),F),k4_scmfsa_2(np__0)) = np__1
                              & r5_scmfsa7b(E,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr3(B,C,D,E,A),F))
                              & r6_scmfsa7b(E,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr3(B,C,D,E,A),F)) )
                           => k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr3(B,C,D,E,A),k1_nat_1(F,np__1)),k4_scmfsa_2(np__0)) = np__1 ) ) ) ) ) ) ) )).

fof(t25_sfmastr3,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] :
              ( m1_scmfsa_2(C)
             => ! [D] :
                  ( m1_scmfsa_2(D)
                 => ! [E] :
                      ( ( v1_ami_3(E,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
                        & v1_scmfsa_4(E)
                        & v1_scmfsa7b(E)
                        & m1_ami_1(E,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
                     => ( ( k20_scmfsa_2(A,k4_scmfsa_2(np__0)) = np__1
                          & r3_sfmastr3(B,C,D,E,A) )
                       => ! [F] :
                            ( m2_subset_1(F,k1_numbers,k5_numbers)
                           => ( r1_xreal_0(F,k2_xcmplx_0(k6_xcmplx_0(k20_scmfsa_2(A,D),k20_scmfsa_2(A,C)),np__1))
                             => ( k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr3(B,C,D,E,A),F),k4_scmfsa_2(np__0)) = np__1
                                & ( r4_scmfsa7b(E,B)
                                 => ( k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr3(B,C,D,E,A),F),B) = k2_xcmplx_0(F,k20_scmfsa_2(A,C))
                                    & r1_xreal_0(k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr3(B,C,D,E,A),F),B),k2_xcmplx_0(k20_scmfsa_2(A,D),np__1)) ) )
                                & k2_xcmplx_0(k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr3(B,C,D,E,A),F),k6_sfmastr1(np__1,k4_subset_1(k2_scmfsa_2,k3_sfmastr1(B,C,D),k2_sf_mastr(E)))),F) = k2_xcmplx_0(k6_xcmplx_0(k20_scmfsa_2(A,D),k20_scmfsa_2(A,C)),np__1) ) ) ) ) ) ) ) ) ) )).

fof(t26_sfmastr3,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] :
              ( m1_scmfsa_2(C)
             => ! [D] :
                  ( m1_scmfsa_2(D)
                 => ! [E] :
                      ( ( v1_ami_3(E,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
                        & v1_scmfsa_4(E)
                        & v1_scmfsa7b(E)
                        & m1_ami_1(E,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
                     => ( ( k20_scmfsa_2(A,k4_scmfsa_2(np__0)) = np__1
                          & r3_sfmastr3(B,C,D,E,A) )
                       => ! [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,k2_sfmastr3(B,C,D,E,A),F),k6_sfmastr1(np__1,k4_subset_1(k2_scmfsa_2,k3_sfmastr1(B,C,D),k2_sf_mastr(E)))),np__0)
                                  & r1_xreal_0(k2_xcmplx_0(k6_xcmplx_0(k20_scmfsa_2(A,D),k20_scmfsa_2(A,C)),np__1),F) )
                              & ~ ( ~ r1_xreal_0(k2_xcmplx_0(k6_xcmplx_0(k20_scmfsa_2(A,D),k20_scmfsa_2(A,C)),np__1),F)
                                  & r1_xreal_0(k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr3(B,C,D,E,A),F),k6_sfmastr1(np__1,k4_subset_1(k2_scmfsa_2,k3_sfmastr1(B,C,D),k2_sf_mastr(E)))),np__0) ) ) ) ) ) ) ) ) ) )).

fof(t27_sfmastr3,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] :
              ( m1_scmfsa_2(C)
             => ! [D] :
                  ( m1_scmfsa_2(D)
                 => ! [E] :
                      ( ( v1_ami_3(E,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
                        & v1_scmfsa_4(E)
                        & v1_scmfsa7b(E)
                        & m1_ami_1(E,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
                     => ! [F] :
                          ( m2_subset_1(F,k1_numbers,k5_numbers)
                         => ( ( k20_scmfsa_2(A,k4_scmfsa_2(np__0)) = np__1
                              & r3_sfmastr3(B,C,D,E,A) )
                           => ( r1_xreal_0(k2_xcmplx_0(k6_xcmplx_0(k20_scmfsa_2(A,D),k20_scmfsa_2(A,C)),np__1),F)
                              | k7_relat_1(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr3(B,C,D,E,A),k1_nat_1(F,np__1)),k2_xboole_0(k4_subset_1(k2_scmfsa_2,k3_sfmastr1(B,C,D),k2_sf_mastr(E)),k3_scmfsa_2)) = k7_relat_1(k3_scmfsa6b(k6_scmfsa6a(E,k9_scmfsa_2(B,k4_scmfsa_2(np__0))),k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr3(B,C,D,E,A),F)),k2_xboole_0(k4_subset_1(k2_scmfsa_2,k3_sfmastr1(B,C,D),k2_sf_mastr(E)),k3_scmfsa_2)) ) ) ) ) ) ) ) ) )).

fof(d8_sfmastr3,axiom,(
    ! [A] :
      ( m1_scmfsa_2(A)
     => ! [B] :
          ( m1_scmfsa_2(B)
         => ! [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) )
                 => k3_sfmastr3(A,B,C,D) = k4_scmfsa6a(k6_scmfsa6a(k6_scmfsa6a(k7_scmfsa6a(k8_scmfsa_2(k6_sfmastr1(np__1,k4_subset_1(k2_scmfsa_2,k3_sfmastr1(A,B,C),k2_sf_mastr(D))),C),k10_scmfsa_2(k6_sfmastr1(np__1,k4_subset_1(k2_scmfsa_2,k3_sfmastr1(A,B,C),k2_sf_mastr(D))),B)),k9_scmfsa_2(k6_sfmastr1(np__1,k4_subset_1(k2_scmfsa_2,k3_sfmastr1(A,B,C),k2_sf_mastr(D))),k4_scmfsa_2(np__0))),k8_scmfsa_2(A,B)),k2_scmfsa_9(k6_sfmastr1(np__1,k4_subset_1(k2_scmfsa_2,k3_sfmastr1(A,B,C),k2_sf_mastr(D))),k6_scmfsa6a(k6_scmfsa6a(D,k9_scmfsa_2(A,k4_scmfsa_2(np__0))),k10_scmfsa_2(k6_sfmastr1(np__1,k4_subset_1(k2_scmfsa_2,k3_sfmastr1(A,B,C),k2_sf_mastr(D))),k4_scmfsa_2(np__0))))) ) ) ) ) )).

fof(t28_sfmastr3,axiom,(
    ! [A] :
      ( m1_scmfsa_2(A)
     => ! [B] :
          ( m1_scmfsa_2(B)
         => ! [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_tarski(k4_subset_1(k2_scmfsa_2,k3_sfmastr1(A,B,C),k2_sf_mastr(D)),k2_sf_mastr(k3_sfmastr3(A,B,C,D))) ) ) ) ) )).

fof(t29_sfmastr3,axiom,(
    ! [A] :
      ( ( ~ v1_sf_mastr(A)
        & m1_scmfsa_2(A) )
     => ! [B] :
          ( m1_scmfsa_2(B)
         => ! [C] :
              ( m1_scmfsa_2(C)
             => ! [D] :
                  ( m1_scmfsa_2(D)
                 => ! [E] :
                      ( ( v1_ami_3(E,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
                        & v1_scmfsa_4(E)
                        & m1_ami_1(E,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
                     => ( r4_scmfsa7b(E,B)
                       => ( A = B
                          | B = k6_sfmastr1(np__1,k4_subset_1(k2_scmfsa_2,k3_sfmastr1(A,C,D),k2_sf_mastr(E)))
                          | r4_scmfsa7b(k3_sfmastr3(A,C,D,E),B) ) ) ) ) ) ) ) )).

fof(t30_sfmastr3,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] :
              ( m1_scmfsa_2(C)
             => ! [D] :
                  ( m1_scmfsa_2(D)
                 => ! [E] :
                      ( ( v1_ami_3(E,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
                        & v1_scmfsa_4(E)
                        & m1_ami_1(E,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,C),k20_scmfsa_2(A,D))
                          | ( ! [F] :
                                ( m1_scmfsa_2(F)
                               => ( r2_hidden(F,k4_subset_1(k2_scmfsa_2,k2_sfmastr1(C,D),k2_sf_mastr(E)))
                                 => ( F = B
                                    | k20_scmfsa_2(k3_scmfsa6b(k3_sfmastr3(B,C,D,E),A),F) = k20_scmfsa_2(A,F) ) ) )
                            & ! [F] :
                                ( m2_scmfsa_2(F)
                               => k21_scmfsa_2(k3_scmfsa6b(k3_sfmastr3(B,C,D,E),A),F) = k21_scmfsa_2(A,F) ) ) ) ) ) ) ) ) ) )).

fof(t31_sfmastr3,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] :
              ( m1_scmfsa_2(C)
             => ! [D] :
                  ( m1_scmfsa_2(D)
                 => ! [E] :
                      ( ( v1_ami_3(E,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
                        & v1_scmfsa_4(E)
                        & v1_scmfsa7b(E)
                        & m1_ami_1(E,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
                     => ! [F] :
                          ( m2_subset_1(F,k1_numbers,k5_numbers)
                         => ( ( k20_scmfsa_2(A,k4_scmfsa_2(np__0)) = np__1
                              & F = k2_xcmplx_0(k6_xcmplx_0(k20_scmfsa_2(A,C),k20_scmfsa_2(A,D)),np__1) )
                           => ( ( ~ r3_sfmastr3(B,D,C,E,A)
                                & ~ v2_scmfsa6b(E) )
                              | k7_relat_1(k3_scmfsa6b(k3_sfmastr3(B,D,C,E),A),k4_subset_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,k2_sfmastr3(B,D,C,E,A),F),k4_subset_1(u1_struct_0(k1_scmfsa_2),k2_scmfsa_2,k3_scmfsa_2)) ) ) ) ) ) ) ) ) )).

fof(t32_sfmastr3,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] :
              ( m1_scmfsa_2(C)
             => ! [D] :
                  ( m1_scmfsa_2(D)
                 => ! [E] :
                      ( ( v1_ami_3(E,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
                        & v1_scmfsa_4(E)
                        & v1_scmfsa7b(E)
                        & m1_ami_1(E,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
                     => ( k20_scmfsa_2(A,k4_scmfsa_2(np__0)) = np__1
                       => ( ( ~ r3_sfmastr3(B,C,D,E,A)
                            & ~ v2_scmfsa6b(E) )
                          | ( r5_scmfsa7b(k3_sfmastr3(B,C,D,E),A)
                            & r6_scmfsa7b(k3_sfmastr3(B,C,D,E),A) ) ) ) ) ) ) ) ) )).

fof(d9_sfmastr3,axiom,(
    ! [A] :
      ( m1_scmfsa_2(A)
     => ! [B] :
          ( m1_scmfsa_2(B)
         => ! [C] :
              ( m1_scmfsa_2(C)
             => ! [D] :
                  ( m2_scmfsa_2(D)
                 => k4_sfmastr3(A,B,C,D) = k5_scmfsa6a(k8_scmfsa_2(C,A),k3_sfmastr3(k6_sfmastr1(np__3,k3_sfmastr1(A,B,C)),A,B,k4_scmfsa6a(k7_scmfsa6a(k16_scmfsa_2(k6_sfmastr1(np__1,k3_sfmastr1(A,B,C)),k6_sfmastr1(np__3,k3_sfmastr1(A,B,C)),D),k16_scmfsa_2(k6_sfmastr1(np__2,k3_sfmastr1(A,B,C)),C,D)),k5_scmfsa8b(k6_sfmastr1(np__2,k3_sfmastr1(A,B,C)),k6_sfmastr1(np__1,k3_sfmastr1(A,B,C)),k2_scmfsa6a(k8_scmfsa_2(C,k6_sfmastr1(np__3,k3_sfmastr1(A,B,C)))),k5_scmfsa_4)))) ) ) ) ) )).

fof(t33_sfmastr3,axiom,(
    ! [A] :
      ( ( ~ v1_sf_mastr(A)
        & m1_scmfsa_2(A) )
     => ! [B] :
          ( m1_scmfsa_2(B)
         => ! [C] :
              ( m1_scmfsa_2(C)
             => ! [D] :
                  ( m2_scmfsa_2(D)
                 => ( A != B
                   => r4_scmfsa7b(k4_sfmastr3(B,C,A,D),B) ) ) ) ) ) )).

fof(t34_sfmastr3,axiom,(
    ! [A] :
      ( ( ~ v1_sf_mastr(A)
        & m1_scmfsa_2(A) )
     => ! [B] :
          ( m1_scmfsa_2(B)
         => ! [C] :
              ( m1_scmfsa_2(C)
             => ! [D] :
                  ( m2_scmfsa_2(D)
                 => r1_tarski(k3_sfmastr1(B,C,A),k2_sf_mastr(k4_sfmastr3(B,C,A,D))) ) ) ) ) )).

fof(t35_sfmastr3,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] :
              ( m1_scmfsa_2(C)
             => ! [D] :
                  ( m1_scmfsa_2(D)
                 => ! [E] :
                      ( m2_scmfsa_2(E)
                     => ( k20_scmfsa_2(A,k4_scmfsa_2(np__0)) = np__1
                       => ( r5_scmfsa7b(k4_sfmastr3(C,D,B,E),A)
                          & r6_scmfsa7b(k4_sfmastr3(C,D,B,E),A) ) ) ) ) ) ) ) )).

fof(t36_sfmastr3,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] :
              ( m1_scmfsa_2(C)
             => ! [D] :
                  ( m1_scmfsa_2(D)
                 => ! [E] :
                      ( m2_scmfsa_2(E)
                     => ( k20_scmfsa_2(A,k4_scmfsa_2(np__0)) = np__1
                       => ( C = B
                          | D = B
                          | ( k21_scmfsa_2(k3_scmfsa6b(k4_sfmastr3(C,D,B,E),A),E) = k21_scmfsa_2(A,E)
                            & k20_scmfsa_2(k3_scmfsa6b(k4_sfmastr3(C,D,B,E),A),C) = k20_scmfsa_2(A,C)
                            & k20_scmfsa_2(k3_scmfsa6b(k4_sfmastr3(C,D,B,E),A),D) = k20_scmfsa_2(A,D) ) ) ) ) ) ) ) ) )).

fof(t37_sfmastr3,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] :
              ( m1_scmfsa_2(C)
             => ! [D] :
                  ( m1_scmfsa_2(D)
                 => ! [E] :
                      ( m2_scmfsa_2(E)
                     => ( ( r1_xreal_0(np__1,k20_scmfsa_2(A,C))
                          & r1_xreal_0(k20_scmfsa_2(A,C),k20_scmfsa_2(A,D))
                          & r1_xreal_0(k20_scmfsa_2(A,D),k3_finseq_1(k21_scmfsa_2(A,E)))
                          & k20_scmfsa_2(A,k4_scmfsa_2(np__0)) = np__1 )
                       => ( C = B
                          | D = B
                          | k20_scmfsa_2(k3_scmfsa6b(k4_sfmastr3(C,D,B,E),A),B) = k1_sfmastr3(k21_scmfsa_2(A,E),k1_int_2(k20_scmfsa_2(A,C)),k1_int_2(k20_scmfsa_2(A,D))) ) ) ) ) ) ) ) )).

fof(d10_sfmastr3,axiom,(
    ! [A] :
      ( m2_scmfsa_2(A)
     => ! [B] :
          ( m1_scmfsa_2(B)
         => ! [C] :
              ( m1_scmfsa_2(C)
             => k5_sfmastr3(A,B,C) = k6_scmfsa6a(k6_scmfsa6a(k7_scmfsa6a(k16_scmfsa_2(k6_sfmastr1(np__1,k2_sfmastr1(B,C)),B,A),k16_scmfsa_2(k6_sfmastr1(np__2,k2_sfmastr1(B,C)),C,A)),k17_scmfsa_2(k6_sfmastr1(np__2,k2_sfmastr1(B,C)),B,A)),k17_scmfsa_2(k6_sfmastr1(np__1,k2_sfmastr1(B,C)),C,A)) ) ) ) )).

fof(t38_sfmastr3,axiom,(
    ! [A] :
      ( m1_scmfsa_2(A)
     => ! [B] :
          ( m1_scmfsa_2(B)
         => ! [C] :
              ( m1_scmfsa_2(C)
             => ! [D] :
                  ( m2_scmfsa_2(D)
                 => ~ ( A != k6_sfmastr1(np__1,k2_sfmastr1(B,C))
                      & A != k6_sfmastr1(np__2,k2_sfmastr1(B,C))
                      & ~ r4_scmfsa7b(k5_sfmastr3(D,B,C),A) ) ) ) ) ) )).

fof(t39_sfmastr3,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_scmfsa_2(B)
         => ! [C] :
              ( m1_scmfsa_2(C)
             => ! [D] :
                  ( m2_scmfsa_2(D)
                 => ( ( r1_xreal_0(np__1,k20_scmfsa_2(A,B))
                      & r1_xreal_0(k20_scmfsa_2(A,B),k3_finseq_1(k21_scmfsa_2(A,D)))
                      & r1_xreal_0(np__1,k20_scmfsa_2(A,C))
                      & r1_xreal_0(k20_scmfsa_2(A,C),k3_finseq_1(k21_scmfsa_2(A,D)))
                      & k20_scmfsa_2(A,k4_scmfsa_2(np__0)) = np__1 )
                   => k21_scmfsa_2(k3_scmfsa6b(k5_sfmastr3(D,B,C),A),D) = k2_funct_7(k2_funct_7(k21_scmfsa_2(A,D),k20_scmfsa_2(A,B),k1_funct_1(k21_scmfsa_2(A,D),k20_scmfsa_2(A,C))),k20_scmfsa_2(A,C),k1_funct_1(k21_scmfsa_2(A,D),k20_scmfsa_2(A,B))) ) ) ) ) ) )).

fof(t40_sfmastr3,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_scmfsa_2(B)
         => ! [C] :
              ( m1_scmfsa_2(C)
             => ! [D] :
                  ( m2_scmfsa_2(D)
                 => ( ( r1_xreal_0(np__1,k20_scmfsa_2(A,B))
                      & r1_xreal_0(k20_scmfsa_2(A,B),k3_finseq_1(k21_scmfsa_2(A,D)))
                      & r1_xreal_0(np__1,k20_scmfsa_2(A,C))
                      & r1_xreal_0(k20_scmfsa_2(A,C),k3_finseq_1(k21_scmfsa_2(A,D)))
                      & k20_scmfsa_2(A,k4_scmfsa_2(np__0)) = np__1 )
                   => ( k1_funct_1(k21_scmfsa_2(k3_scmfsa6b(k5_sfmastr3(D,B,C),A),D),k20_scmfsa_2(A,B)) = k1_funct_1(k21_scmfsa_2(A,D),k20_scmfsa_2(A,C))
                      & k1_funct_1(k21_scmfsa_2(k3_scmfsa6b(k5_sfmastr3(D,B,C),A),D),k20_scmfsa_2(A,C)) = k1_funct_1(k21_scmfsa_2(A,D),k20_scmfsa_2(A,B)) ) ) ) ) ) ) )).

fof(t41_sfmastr3,axiom,(
    ! [A] :
      ( m1_scmfsa_2(A)
     => ! [B] :
          ( m1_scmfsa_2(B)
         => ! [C] :
              ( m2_scmfsa_2(C)
             => r1_tarski(k2_sfmastr1(A,B),k2_sf_mastr(k5_sfmastr3(C,A,B))) ) ) ) )).

fof(t42_sfmastr3,axiom,(
    ! [A] :
      ( m1_scmfsa_2(A)
     => ! [B] :
          ( m1_scmfsa_2(B)
         => ! [C] :
              ( m2_scmfsa_2(C)
             => k4_sf_mastr(k5_sfmastr3(C,A,B)) = k1_tarski(C) ) ) ) )).

fof(d11_sfmastr3,axiom,(
    ! [A] :
      ( m2_scmfsa_2(A)
     => k6_sfmastr3(A) = k5_scmfsa6a(k18_scmfsa_2(k7_sfmastr1(np__1,k5_sfmastr3(A,k6_sfmastr1(np__1,k1_subset_1(k2_scmfsa_2)),k6_sfmastr1(np__2,k1_subset_1(k2_scmfsa_2)))),A),k3_sfmastr3(k6_sfmastr1(np__1,k1_subset_1(k2_scmfsa_2)),k4_scmfsa_2(np__0),k7_sfmastr1(np__1,k5_sfmastr3(A,k6_sfmastr1(np__1,k1_subset_1(k2_scmfsa_2)),k6_sfmastr1(np__2,k1_subset_1(k2_scmfsa_2)))),k4_scmfsa6a(k4_sfmastr3(k6_sfmastr1(np__1,k1_subset_1(k2_scmfsa_2)),k7_sfmastr1(np__1,k5_sfmastr3(A,k6_sfmastr1(np__1,k1_subset_1(k2_scmfsa_2)),k6_sfmastr1(np__2,k1_subset_1(k2_scmfsa_2)))),k6_sfmastr1(np__2,k1_subset_1(k2_scmfsa_2)),A),k5_sfmastr3(A,k6_sfmastr1(np__1,k1_subset_1(k2_scmfsa_2)),k6_sfmastr1(np__2,k1_subset_1(k2_scmfsa_2)))))) ) )).

fof(t43_sfmastr3,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] :
          ( m2_scmfsa_2(B)
         => ! [C] :
              ( m1_subset_1(C,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
             => ( C = k3_scmfsa6b(k6_sfmastr3(B),A)
               => ( r1_sfmastr3(k21_scmfsa_2(C,B),np__1,k3_finseq_1(k21_scmfsa_2(C,B)))
                  & ? [D] :
                      ( v1_funct_1(D)
                      & v1_funct_2(D,k4_finseq_1(k21_scmfsa_2(A,B)),k4_finseq_1(k21_scmfsa_2(A,B)))
                      & v3_funct_2(D,k4_finseq_1(k21_scmfsa_2(A,B)),k4_finseq_1(k21_scmfsa_2(A,B)))
                      & m2_relset_1(D,k4_finseq_1(k21_scmfsa_2(A,B)),k4_finseq_1(k21_scmfsa_2(A,B)))
                      & k21_scmfsa_2(C,B) = k1_partfun1(k4_finseq_1(k21_scmfsa_2(A,B)),k4_finseq_1(k21_scmfsa_2(A,B)),k5_numbers,k4_numbers,D,k21_scmfsa_2(A,B)) ) ) ) ) ) ) )).

fof(dt_k1_sfmastr3,axiom,(
    ! [A,B,C] :
      ( ( m1_finseq_1(A,k4_numbers)
        & m1_subset_1(B,k5_numbers)
        & m1_subset_1(C,k5_numbers) )
     => m2_subset_1(k1_sfmastr3(A,B,C),k1_numbers,k5_numbers) ) )).

fof(dt_k2_sfmastr3,axiom,(
    ! [A,B,C,D,E] :
      ( ( m1_scmfsa_2(A)
        & m1_scmfsa_2(B)
        & m1_scmfsa_2(C)
        & 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)
        & m1_subset_1(E,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))) )
     => ( v1_funct_1(k2_sfmastr3(A,B,C,D,E))
        & v1_funct_2(k2_sfmastr3(A,B,C,D,E),k5_numbers,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
        & m2_relset_1(k2_sfmastr3(A,B,C,D,E),k5_numbers,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))) ) ) )).

fof(dt_k3_sfmastr3,axiom,(
    ! [A,B,C,D] :
      ( ( m1_scmfsa_2(A)
        & m1_scmfsa_2(B)
        & m1_scmfsa_2(C)
        & 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) )
     => ( v1_ami_3(k3_sfmastr3(A,B,C,D),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & v1_scmfsa_4(k3_sfmastr3(A,B,C,D))
        & m1_ami_1(k3_sfmastr3(A,B,C,D),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) ) )).

fof(dt_k4_sfmastr3,axiom,(
    ! [A,B,C,D] :
      ( ( m1_scmfsa_2(A)
        & m1_scmfsa_2(B)
        & m1_scmfsa_2(C)
        & m2_scmfsa_2(D) )
     => ( v1_ami_3(k4_sfmastr3(A,B,C,D),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & v1_scmfsa_4(k4_sfmastr3(A,B,C,D))
        & m1_ami_1(k4_sfmastr3(A,B,C,D),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) ) )).

fof(dt_k5_sfmastr3,axiom,(
    ! [A,B,C] :
      ( ( m2_scmfsa_2(A)
        & m1_scmfsa_2(B)
        & m1_scmfsa_2(C) )
     => ( v1_ami_3(k5_sfmastr3(A,B,C),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & v1_scmfsa_4(k5_sfmastr3(A,B,C))
        & m1_ami_1(k5_sfmastr3(A,B,C),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) ) )).

fof(dt_k6_sfmastr3,axiom,(
    ! [A] :
      ( m2_scmfsa_2(A)
     => ( v1_ami_3(k6_sfmastr3(A),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & v1_scmfsa_4(k6_sfmastr3(A))
        & m1_ami_1(k6_sfmastr3(A),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) ) )).
%------------------------------------------------------------------------------