SET007 Axioms: SET007+898.ax


%------------------------------------------------------------------------------
% File     : SET007+898 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Stirling Numbers of the Second Kind
% 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    : stirl2_1 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  123 (   1 unit)
%            Number of atoms       :  908 ( 164 equality)
%            Maximal formula depth :   27 (   9 average)
%            Number of connectives :  870 (  85 ~  ;  10  |; 407  &)
%                                         (  22 <=>; 346 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   35 (   0 propositional; 1-3 arity)
%            Number of functors    :  109 (  41 constant; 0-6 arity)
%            Number of variables   :  354 (   0 singleton; 333 !;  21 ?)
%            Maximal term depth    :    7 (   1 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_stirl2_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,A)
         => ( v4_ordinal2(B)
            & v1_xcmplx_0(B)
            & v1_finset_1(B)
            & v1_xreal_0(B)
            & ~ v3_xreal_0(B)
            & v1_int_1(B) ) ) ) )).

fof(fc1_stirl2_1,axiom,(
    ! [A,B,C,D] :
      ( ( m1_subset_1(B,k1_zfmisc_1(k5_numbers))
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B) )
     => ( v4_ordinal2(k1_funct_1(C,D))
        & v1_xcmplx_0(k1_funct_1(C,D))
        & v1_finset_1(k1_funct_1(C,D))
        & v1_xreal_0(k1_funct_1(C,D))
        & ~ v3_xreal_0(k1_funct_1(C,D))
        & v1_int_1(k1_funct_1(C,D)) ) ) )).

fof(t1_stirl2_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(k5_numbers)) )
     => k10_cqc_sim1(A) = k1_henmodel(A) ) )).

fof(t2_stirl2_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(k5_numbers)) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(k5_numbers)) )
         => k3_square_1(k10_cqc_sim1(A),k10_cqc_sim1(B)) = k10_cqc_sim1(k4_subset_1(k5_numbers,A,B)) ) ) )).

fof(t3_stirl2_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k5_numbers))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k5_numbers))
         => r1_xreal_0(k3_square_1(k1_henmodel(A),k1_henmodel(B)),k1_henmodel(k4_subset_1(k5_numbers,A,B))) ) ) )).

fof(t4_stirl2_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k5_numbers))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k5_numbers))
         => ( ~ r2_hidden(k1_henmodel(A),k5_subset_1(k5_numbers,A,B))
           => k1_henmodel(A) = k1_henmodel(k6_subset_1(k5_numbers,A,B)) ) ) ) )).

fof(t5_stirl2_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ( k1_henmodel(k1_stirl2_1(A)) = A
        & k10_cqc_sim1(k1_stirl2_1(A)) = A ) ) )).

fof(t6_stirl2_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( k1_henmodel(k2_stirl2_1(A,B)) = k3_square_1(A,B)
            & k10_cqc_sim1(k2_stirl2_1(A,B)) = k3_square_1(A,B) ) ) ) )).

fof(t7_stirl2_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => k1_henmodel(k3_stirl2_1(A,B,C)) = k3_square_1(A,k3_square_1(B,C)) ) ) ) )).

fof(t8_stirl2_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => m1_subset_1(A,k1_zfmisc_1(k5_numbers)) ) )).

fof(t9_stirl2_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(k5_numbers)) )
         => ( r1_tarski(B,A)
           => m2_subset_1(k10_binop_2(A,np__1),k1_numbers,k5_numbers) ) ) ) )).

fof(t10_stirl2_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( r2_hidden(A,B)
           => ( r1_xreal_0(A,k10_binop_2(B,np__1))
              & m2_subset_1(k10_binop_2(B,np__1),k1_numbers,k5_numbers) ) ) ) ) )).

fof(t11_stirl2_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => k1_henmodel(A) = np__0 ) )).

fof(t12_stirl2_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(k5_numbers)) )
         => ( r1_tarski(B,A)
           => r1_xreal_0(k1_henmodel(B),k10_binop_2(A,np__1)) ) ) ) )).

fof(t13_stirl2_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(k5_numbers)) )
         => ~ ( r1_tarski(B,A)
              & B != k2_setwiseo(k1_numbers,k10_binop_2(A,np__1))
              & r1_xreal_0(k10_binop_2(A,np__1),k1_henmodel(B)) ) ) ) )).

fof(t14_stirl2_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k5_numbers))
         => ( r1_tarski(B,A)
           => ( r1_xreal_0(A,np__0)
              | r1_xreal_0(k1_henmodel(B),k10_binop_2(A,np__1)) ) ) ) ) )).

fof(d1_stirl2_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,B)
                & m2_relset_1(C,A,B) )
             => ( v1_stirl2_1(C,A,B)
              <=> ( ( A = np__0
                   => B = np__0 )
                  & ( B = np__0
                   => A = np__0 )
                  & ! [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ! [E] :
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                         => ~ ( r2_hidden(D,k5_relset_1(A,B,C))
                              & r2_hidden(E,k5_relset_1(A,B,C))
                              & ~ r1_xreal_0(E,D)
                              & r1_xreal_0(k1_henmodel(k4_stirl2_1(A,B,C,k1_stirl2_1(E))),k1_henmodel(k4_stirl2_1(A,B,C,k1_stirl2_1(D)))) ) ) ) ) ) ) ) ) )).

fof(t15_stirl2_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,B)
                & m2_relset_1(C,A,B) )
             => ( ( A = np__0
                  & B = np__0 )
               => ( v2_funct_2(C,A,B)
                  & v1_stirl2_1(C,A,B) ) ) ) ) ) )).

fof(t16_stirl2_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,B,A)
                    & m2_relset_1(D,B,A) )
                 => ( ~ r1_xreal_0(B,np__0)
                   => r1_xreal_0(k1_henmodel(k4_stirl2_1(B,A,D,k1_stirl2_1(C))),k10_binop_2(B,np__1)) ) ) ) ) ) )).

fof(t17_stirl2_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,B)
                & m2_relset_1(C,A,B) )
             => ( v2_funct_2(C,A,B)
               => r1_xreal_0(B,A) ) ) ) ) )).

fof(t18_stirl2_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,B)
                & m2_relset_1(C,A,B) )
             => ( ( v2_funct_2(C,A,B)
                  & v1_stirl2_1(C,A,B) )
               => ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ( ~ r1_xreal_0(B,D)
                     => r1_xreal_0(D,k1_henmodel(k4_stirl2_1(A,B,C,k1_stirl2_1(D)))) ) ) ) ) ) ) )).

fof(t19_stirl2_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,B,A)
                & m2_relset_1(C,B,A) )
             => ( ( v2_funct_2(C,B,A)
                  & v1_stirl2_1(C,B,A) )
               => ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ( ~ r1_xreal_0(A,D)
                     => r1_xreal_0(k1_henmodel(k4_stirl2_1(B,A,C,k1_stirl2_1(D))),k9_binop_2(k10_binop_2(B,A),D)) ) ) ) ) ) ) )).

fof(t20_stirl2_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,B)
                & m2_relset_1(C,A,B) )
             => ( ( v2_funct_2(C,A,B)
                  & v1_stirl2_1(C,A,B)
                  & A = B )
               => C = k6_partfun1(A) ) ) ) ) )).

fof(t21_stirl2_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,B,A)
                & m2_relset_1(C,B,A) )
             => ( C = k6_partfun1(B)
               => ( r1_xreal_0(B,np__0)
                  | v1_stirl2_1(C,B,A) ) ) ) ) ) )).

fof(t22_stirl2_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ~ ( ( A = np__0
               => B = np__0 )
              & ( B = np__0
               => A = np__0 )
              & ! [C] :
                  ( ( v1_funct_1(C)
                    & v1_funct_2(C,A,B)
                    & m2_relset_1(C,A,B) )
                 => ~ v1_stirl2_1(C,A,B) ) ) ) ) )).

fof(t23_stirl2_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ~ ( ( A = np__0
               => B = np__0 )
              & ( B = np__0
               => A = np__0 )
              & r1_xreal_0(B,A)
              & ! [C] :
                  ( ( v1_funct_1(C)
                    & v1_funct_2(C,A,B)
                    & m2_relset_1(C,A,B) )
                 => ~ ( v2_funct_2(C,A,B)
                      & v1_stirl2_1(C,A,B) ) ) ) ) ) )).

fof(t26_stirl2_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => k6_stirl2_1(A,A) = k4_ordinal2 ) )).

fof(t27_stirl2_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ( A != np__0
       => k6_stirl2_1(np__0,A) = np__0 ) ) )).

fof(t28_stirl2_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ( k6_stirl2_1(np__0,A) = k4_ordinal2
      <=> A = np__0 ) ) )).

fof(t29_stirl2_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( ~ r1_xreal_0(B,A)
           => k6_stirl2_1(A,B) = np__0 ) ) ) )).

fof(t30_stirl2_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ( k6_stirl2_1(A,np__0) = k4_ordinal2
      <=> A = np__0 ) ) )).

fof(t31_stirl2_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ( A != np__0
       => k6_stirl2_1(A,np__0) = np__0 ) ) )).

fof(t32_stirl2_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ( A != np__0
       => k6_stirl2_1(A,np__1) = k4_ordinal2 ) ) )).

fof(t33_stirl2_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( ~ ( ( ( r1_xreal_0(np__1,A)
                    & r1_xreal_0(A,B) )
                  | A = B )
                & r1_xreal_0(k6_stirl2_1(B,A),np__0) )
            & ~ ( ~ r1_xreal_0(k6_stirl2_1(B,A),np__0)
                & ~ ( r1_xreal_0(np__1,A)
                    & r1_xreal_0(A,B) )
                & A != B ) ) ) ) )).

fof(t34_stirl2_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k23_binop_2(A,np__1),k23_binop_2(B,np__1))
                & m2_relset_1(C,k23_binop_2(A,np__1),k23_binop_2(B,np__1)) )
             => ( ( v2_funct_2(C,k23_binop_2(A,np__1),k23_binop_2(B,np__1))
                  & v1_stirl2_1(C,k23_binop_2(A,np__1),k23_binop_2(B,np__1))
                  & k4_stirl2_1(k23_binop_2(A,np__1),k23_binop_2(B,np__1),C,k2_setwiseo(k23_binop_2(B,np__1),k5_stirl2_1(k23_binop_2(A,np__1),k23_binop_2(B,np__1),C,A))) = k1_stirl2_1(A) )
               => k5_stirl2_1(k23_binop_2(A,np__1),k23_binop_2(B,np__1),C,A) = B ) ) ) ) )).

fof(t35_stirl2_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k23_binop_2(A,np__1),B)
                & m2_relset_1(C,k23_binop_2(A,np__1),B) )
             => ~ ( B != np__0
                  & k4_stirl2_1(k23_binop_2(A,np__1),B,C,k1_tarski(k5_stirl2_1(k23_binop_2(A,np__1),B,C,A))) != k1_stirl2_1(A)
                  & ! [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ~ ( r2_hidden(D,k4_stirl2_1(k23_binop_2(A,np__1),B,C,k1_tarski(k5_stirl2_1(k23_binop_2(A,np__1),B,C,A))))
                          & D != A ) ) ) ) ) ) )).

fof(t36_stirl2_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,A,B)
                        & m2_relset_1(E,A,B) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,k23_binop_2(A,C),k23_binop_2(B,D))
                            & m2_relset_1(F,k23_binop_2(A,C),k23_binop_2(B,D)) )
                         => ( ( v1_stirl2_1(F,k23_binop_2(A,C),k23_binop_2(B,D))
                              & E = k2_partfun1(k23_binop_2(A,C),k23_binop_2(B,D),F,A) )
                           => ! [G] :
                                ( m2_subset_1(G,k1_numbers,k5_numbers)
                               => ! [H] :
                                    ( m2_subset_1(H,k1_numbers,k5_numbers)
                                   => ~ ( r2_hidden(G,k5_relset_1(A,B,E))
                                        & r2_hidden(H,k5_relset_1(A,B,E))
                                        & ~ r1_xreal_0(H,G)
                                        & r1_xreal_0(k1_henmodel(k4_stirl2_1(A,B,E,k1_stirl2_1(H))),k1_henmodel(k4_stirl2_1(A,B,E,k1_stirl2_1(G)))) ) ) ) ) ) ) ) ) ) ) )).

fof(t37_stirl2_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k23_binop_2(A,np__1),k23_binop_2(B,np__1))
                & m2_relset_1(C,k23_binop_2(A,np__1),k23_binop_2(B,np__1)) )
             => ( ( v2_funct_2(C,k23_binop_2(A,np__1),k23_binop_2(B,np__1))
                  & v1_stirl2_1(C,k23_binop_2(A,np__1),k23_binop_2(B,np__1))
                  & k4_stirl2_1(k23_binop_2(A,np__1),k23_binop_2(B,np__1),C,k2_setwiseo(k23_binop_2(B,np__1),k5_stirl2_1(k23_binop_2(A,np__1),k23_binop_2(B,np__1),C,A))) = k1_stirl2_1(A) )
               => ( r1_tarski(k5_relset_1(k23_binop_2(A,np__1),k23_binop_2(B,np__1),k2_partfun1(k23_binop_2(A,np__1),k23_binop_2(B,np__1),C,A)),B)
                  & ! [D] :
                      ( ( v1_funct_1(D)
                        & v1_funct_2(D,A,B)
                        & m2_relset_1(D,A,B) )
                     => ( D = k2_partfun1(k23_binop_2(A,np__1),k23_binop_2(B,np__1),C,A)
                       => ( v2_funct_2(D,A,B)
                          & v1_stirl2_1(D,A,B) ) ) ) ) ) ) ) ) )).

fof(t38_stirl2_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k23_binop_2(A,np__1),B)
                & m2_relset_1(C,k23_binop_2(A,np__1),B) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,B)
                    & m2_relset_1(D,A,B) )
                 => ( ( v2_funct_2(C,k23_binop_2(A,np__1),B)
                      & v1_stirl2_1(C,k23_binop_2(A,np__1),B)
                      & k2_partfun1(k23_binop_2(A,np__1),B,C,A) = D )
                   => ( k4_stirl2_1(k23_binop_2(A,np__1),B,C,k1_tarski(k5_stirl2_1(k23_binop_2(A,np__1),B,C,A))) = k1_stirl2_1(A)
                      | ( v2_funct_2(D,A,B)
                        & v1_stirl2_1(D,A,B) ) ) ) ) ) ) ) )).

fof(t39_stirl2_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,B)
                    & m2_relset_1(D,A,B) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k23_binop_2(A,np__1),k23_binop_2(B,C))
                        & m2_relset_1(E,k23_binop_2(A,np__1),k23_binop_2(B,C)) )
                     => ( ( v2_funct_2(D,A,B)
                          & v1_stirl2_1(D,A,B)
                          & D = k2_partfun1(k23_binop_2(A,np__1),k23_binop_2(B,C),E,A) )
                       => ! [F] :
                            ( m2_subset_1(F,k1_numbers,k5_numbers)
                           => ! [G] :
                                ( m2_subset_1(G,k1_numbers,k5_numbers)
                               => ~ ( r2_hidden(F,k5_relset_1(k23_binop_2(A,np__1),k23_binop_2(B,C),E))
                                    & r2_hidden(G,k5_relset_1(k23_binop_2(A,np__1),k23_binop_2(B,C),E))
                                    & ~ r1_xreal_0(G,F)
                                    & r1_xreal_0(k1_henmodel(k4_stirl2_1(k23_binop_2(A,np__1),k23_binop_2(B,C),E,k1_stirl2_1(G))),k1_henmodel(k4_stirl2_1(k23_binop_2(A,np__1),k23_binop_2(B,C),E,k1_stirl2_1(F)))) ) ) ) ) ) ) ) ) ) )).

fof(t40_stirl2_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,B)
                & m2_relset_1(C,A,B) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k23_binop_2(A,np__1),k23_binop_2(B,np__1))
                    & m2_relset_1(D,k23_binop_2(A,np__1),k23_binop_2(B,np__1)) )
                 => ( ( v2_funct_2(C,A,B)
                      & v1_stirl2_1(C,A,B)
                      & C = k2_partfun1(k23_binop_2(A,np__1),k23_binop_2(B,np__1),D,A)
                      & k5_stirl2_1(k23_binop_2(A,np__1),k23_binop_2(B,np__1),D,A) = B )
                   => ( v2_funct_2(D,k23_binop_2(A,np__1),k23_binop_2(B,np__1))
                      & v1_stirl2_1(D,k23_binop_2(A,np__1),k23_binop_2(B,np__1))
                      & k4_stirl2_1(k23_binop_2(A,np__1),k23_binop_2(B,np__1),D,k2_setwiseo(k23_binop_2(B,np__1),k5_stirl2_1(k23_binop_2(A,np__1),k23_binop_2(B,np__1),D,A))) = k1_stirl2_1(A) ) ) ) ) ) ) )).

fof(t41_stirl2_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,B)
                & m2_relset_1(C,A,B) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k23_binop_2(A,np__1),B)
                    & m2_relset_1(D,k23_binop_2(A,np__1),B) )
                 => ( ( v2_funct_2(C,A,B)
                      & v1_stirl2_1(C,A,B)
                      & C = k2_partfun1(k23_binop_2(A,np__1),B,D,A) )
                   => ( r1_xreal_0(B,k5_stirl2_1(k23_binop_2(A,np__1),B,D,A))
                      | ( v2_funct_2(D,k23_binop_2(A,np__1),B)
                        & v1_stirl2_1(D,k23_binop_2(A,np__1),B)
                        & k4_stirl2_1(k23_binop_2(A,np__1),B,D,k1_tarski(k5_stirl2_1(k23_binop_2(A,np__1),B,D,A))) != k1_stirl2_1(A) ) ) ) ) ) ) ) )).

fof(d3_stirl2_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_finset_1(B)
            & m1_ordinal1(B,A) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),A)
                & m2_relset_1(C,k2_zfmisc_1(A,A),A) )
             => ( ( v1_setwiseo(C,A)
                  | r1_xreal_0(np__1,k1_afinsq_1(B)) )
               => ! [D] :
                    ( m1_subset_1(D,A)
                   => ( ( ( v1_setwiseo(C,A)
                          & k1_afinsq_1(B) = np__0 )
                       => ( D = k7_stirl2_1(A,B,C)
                        <=> D = k3_binop_1(A,C) ) )
                      & ( ~ ( v1_setwiseo(C,A)
                            & k1_afinsq_1(B) = np__0 )
                       => ( D = k7_stirl2_1(A,B,C)
                        <=> ? [E] :
                              ( v1_funct_1(E)
                              & v1_funct_2(E,k5_numbers,A)
                              & m2_relset_1(E,k5_numbers,A)
                              & k8_funct_2(k5_numbers,A,E,np__0) = k1_funct_1(B,np__0)
                              & ! [F] :
                                  ( m2_subset_1(F,k1_numbers,k5_numbers)
                                 => ( ~ r1_xreal_0(k1_afinsq_1(B),k23_binop_2(F,np__1))
                                   => k8_funct_2(k5_numbers,A,E,k23_binop_2(F,np__1)) = k1_binop_1(C,k8_funct_2(k5_numbers,A,E,F),k1_funct_1(B,k23_binop_2(F,np__1))) ) )
                              & D = k1_funct_1(E,k10_binop_2(k1_afinsq_1(B),np__1)) ) ) ) ) ) ) ) ) ) )).

fof(t44_stirl2_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k2_zfmisc_1(A,A),A)
            & m2_relset_1(B,k2_zfmisc_1(A,A),A) )
         => ! [C] :
              ( m1_subset_1(C,A)
             => k7_stirl2_1(A,k9_afinsq_1(A,C),B) = C ) ) ) )).

fof(t45_stirl2_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_finset_1(B)
            & m1_ordinal1(B,A) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),A)
                & m2_relset_1(C,k2_zfmisc_1(A,A),A) )
             => ! [D] :
                  ( m1_subset_1(D,A)
                 => ( ~ ( ~ v1_setwiseo(C,A)
                        & r1_xreal_0(k1_afinsq_1(B),np__0) )
                   => k7_stirl2_1(A,k5_afinsq_1(A,B,k9_afinsq_1(A,D)),C) = k2_binop_1(A,A,A,C,k7_stirl2_1(A,B,C),D) ) ) ) ) ) )).

fof(t46_stirl2_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_finset_1(B)
            & m1_ordinal1(B,A) )
         => ~ ( B != k4_afinsq_1(A)
              & ! [C] :
                  ( ( v1_finset_1(C)
                    & m1_ordinal1(C,A) )
                 => ! [D] :
                      ( m1_subset_1(D,A)
                     => B != k5_afinsq_1(A,C,k9_afinsq_1(A,D)) ) ) ) ) ) )).

fof(t47_stirl2_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_finset_1(B)
            & m1_ordinal1(B,A) )
         => ! [C] :
              ( ( v1_finset_1(C)
                & m1_ordinal1(C,A) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k2_zfmisc_1(A,A),A)
                    & m2_relset_1(D,k2_zfmisc_1(A,A),A) )
                 => ( v2_binop_1(D,A)
                   => ( ( ~ v1_setwiseo(D,A)
                        & ~ ( r1_xreal_0(np__1,k1_afinsq_1(B))
                            & r1_xreal_0(np__1,k1_afinsq_1(C)) ) )
                      | k7_stirl2_1(A,k5_afinsq_1(A,B,C),D) = k2_binop_1(A,A,A,D,k7_stirl2_1(A,B,D),k7_stirl2_1(A,C,D)) ) ) ) ) ) ) )).

fof(t48_stirl2_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k2_zfmisc_1(A,A),A)
            & m2_relset_1(B,k2_zfmisc_1(A,A),A) )
         => ! [C] :
              ( m1_subset_1(C,A)
             => ! [D] :
                  ( m1_subset_1(D,A)
                 => k7_stirl2_1(A,k8_stirl2_1(A,C,D),B) = k2_binop_1(A,A,A,B,C,D) ) ) ) ) )).

fof(t49_stirl2_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k2_zfmisc_1(A,A),A)
            & m2_relset_1(B,k2_zfmisc_1(A,A),A) )
         => ! [C] :
              ( m1_subset_1(C,A)
             => ! [D] :
                  ( m1_subset_1(D,A)
                 => ! [E] :
                      ( m1_subset_1(E,A)
                     => k7_stirl2_1(A,k9_stirl2_1(A,C,D,E),B) = k2_binop_1(A,A,A,B,k2_binop_1(A,A,A,B,C,D),E) ) ) ) ) ) )).

fof(d4_stirl2_1,axiom,(
    ! [A] :
      ( ( v1_finset_1(A)
        & m1_ordinal1(A,k5_numbers) )
     => k10_stirl2_1(A) = k7_stirl2_1(k5_numbers,A,k47_binop_2) ) )).

fof(t50_stirl2_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_finset_1(B)
            & m1_ordinal1(B,k5_numbers) )
         => ( ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => ( r2_hidden(C,k2_afinsq_1(B))
                 => r1_xreal_0(k11_stirl2_1(B,C),A) ) )
           => r1_xreal_0(k10_stirl2_1(B),k24_binop_2(k1_afinsq_1(B),A)) ) ) ) )).

fof(t51_stirl2_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_finset_1(B)
            & m1_ordinal1(B,k5_numbers) )
         => ( ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => ( r2_hidden(C,k2_afinsq_1(B))
                 => r1_xreal_0(A,k11_stirl2_1(B,C)) ) )
           => r1_xreal_0(k24_binop_2(k1_afinsq_1(B),A),k10_stirl2_1(B)) ) ) ) )).

fof(t52_stirl2_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_finset_1(B)
            & m1_ordinal1(B,k5_numbers) )
         => ~ ( ~ r1_xreal_0(k1_afinsq_1(B),np__0)
              & ? [C] :
                  ( r2_hidden(C,k2_afinsq_1(B))
                  & k11_stirl2_1(B,C) = A )
              & ~ r1_xreal_0(A,k10_stirl2_1(B)) ) ) ) )).

fof(t53_stirl2_1,axiom,(
    ! [A] :
      ( ( v1_finset_1(A)
        & m1_ordinal1(A,k5_numbers) )
     => ( k10_stirl2_1(A) = np__0
      <=> ( k1_afinsq_1(A) = np__0
          | ! [B] :
              ( m2_subset_1(B,k1_numbers,k5_numbers)
             => ( r2_hidden(B,k2_afinsq_1(A))
               => k11_stirl2_1(A,B) = np__0 ) ) ) ) ) )).

fof(t54_stirl2_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => k2_xboole_0(k3_tarski(k2_relat_1(k7_relat_1(A,B))),k1_funct_1(A,B)) = k3_tarski(k2_relat_1(k7_relat_1(A,k23_binop_2(B,np__1)))) ) ) )).

fof(t56_stirl2_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => k6_stirl2_1(k23_binop_2(A,np__1),k23_binop_2(B,np__1)) = k23_binop_2(k24_binop_2(k23_binop_2(B,np__1),k6_stirl2_1(A,k23_binop_2(B,np__1))),k6_stirl2_1(A,B)) ) ) )).

fof(t57_stirl2_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ( r1_xreal_0(np__1,A)
       => k6_stirl2_1(A,np__2) = k11_binop_2(k12_binop_2(np__1,np__2),k10_binop_2(k3_newton(np__2,A),np__2)) ) ) )).

fof(t58_stirl2_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ( r1_xreal_0(np__2,A)
       => k6_stirl2_1(A,np__3) = k11_binop_2(k12_binop_2(np__1,np__6),k9_binop_2(k10_binop_2(k3_newton(np__3,A),k11_binop_2(np__3,k3_newton(np__2,A))),np__3)) ) ) )).

fof(t59_stirl2_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ( r1_xreal_0(np__3,A)
       => k6_stirl2_1(A,np__4) = k11_binop_2(k12_binop_2(np__1,np__24),k10_binop_2(k9_binop_2(k10_binop_2(k3_newton(np__4,A),k11_binop_2(np__4,k3_newton(np__3,A))),k11_binop_2(np__6,k3_newton(np__2,A))),np__4)) ) ) )).

fof(t60_stirl2_1,axiom,
    ( k11_newton(np__3) = np__6
    & k11_newton(np__4) = np__24 )).

fof(t61_stirl2_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ( k8_newton(np__1,A) = A
        & k8_newton(np__2,A) = k12_binop_2(k11_binop_2(A,k10_binop_2(A,np__1)),np__2)
        & k8_newton(np__3,A) = k12_binop_2(k11_binop_2(k11_binop_2(A,k10_binop_2(A,np__1)),k10_binop_2(A,np__2)),np__6)
        & k8_newton(np__4,A) = k12_binop_2(k11_binop_2(k11_binop_2(k11_binop_2(A,k10_binop_2(A,np__1)),k10_binop_2(A,np__2)),k10_binop_2(A,np__3)),np__24) ) ) )).

fof(t62_stirl2_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => k6_stirl2_1(k23_binop_2(A,np__1),A) = k8_newton(np__2,k23_binop_2(A,np__1)) ) )).

fof(t63_stirl2_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => k6_stirl2_1(k23_binop_2(A,np__2),A) = k9_binop_2(k11_binop_2(np__3,k8_newton(np__4,k23_binop_2(A,np__2))),k8_newton(np__3,k23_binop_2(A,np__2))) ) )).

fof(t64_stirl2_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( k2_relat_1(k7_relat_1(A,k4_xboole_0(k1_relat_1(A),k10_relat_1(A,k1_tarski(B))))) = k4_xboole_0(k2_relat_1(A),k1_tarski(B))
          & ! [C] :
              ( C != B
             => k10_relat_1(k7_relat_1(A,k4_xboole_0(k1_relat_1(A),k10_relat_1(A,k1_tarski(B)))),k1_tarski(C)) = k10_relat_1(A,k1_tarski(C)) ) ) ) )).

fof(t65_stirl2_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B,C] :
          ( ( k1_card_1(B) = k23_binop_2(A,np__1)
            & r2_hidden(C,B) )
         => k1_card_1(k4_xboole_0(B,k1_tarski(C))) = A ) ) )).

fof(t66_stirl2_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k5_numbers))
     => ~ ( v1_finset_1(A)
          & ! [B] :
              ( m2_subset_1(B,k1_numbers,k5_numbers)
             => ? [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                  & r2_hidden(C,A)
                  & ~ r1_xreal_0(C,B) ) ) ) ) )).

fof(t67_stirl2_1,axiom,(
    ! [A,B,C,D] :
      ~ ( ( v1_xboole_0(B)
         => v1_xboole_0(A) )
        & ~ r2_hidden(C,A)
        & ? [E] :
            ( v1_funct_1(E)
            & v1_funct_2(E,A,B)
            & m2_relset_1(E,A,B)
            & ! [F] :
                ( ( v1_funct_1(F)
                  & v1_funct_2(F,k2_xboole_0(A,k1_tarski(C)),k2_xboole_0(B,k1_tarski(D)))
                  & m2_relset_1(F,k2_xboole_0(A,k1_tarski(C)),k2_xboole_0(B,k1_tarski(D))) )
               => ~ ( k2_partfun1(k2_xboole_0(A,k1_tarski(C)),k2_xboole_0(B,k1_tarski(D)),F,A) = E
                    & k1_funct_1(F,C) = D ) ) ) ) )).

fof(t68_stirl2_1,axiom,(
    ! [A,B,C,D] :
      ( ( v1_xboole_0(B)
       => v1_xboole_0(A) )
     => ! [E] :
          ( ( v1_funct_1(E)
            & v1_funct_2(E,A,B)
            & m2_relset_1(E,A,B) )
         => ! [F] :
              ( ( v1_funct_1(F)
                & v1_funct_2(F,k2_xboole_0(A,k1_tarski(C)),k2_xboole_0(B,k1_tarski(D)))
                & m2_relset_1(F,k2_xboole_0(A,k1_tarski(C)),k2_xboole_0(B,k1_tarski(D))) )
             => ( ( k2_partfun1(k2_xboole_0(A,k1_tarski(C)),k2_xboole_0(B,k1_tarski(D)),F,A) = E
                  & k1_funct_1(F,C) = D )
               => ( ( v2_funct_2(E,A,B)
                   => v2_funct_2(F,k2_xboole_0(A,k1_tarski(C)),k2_xboole_0(B,k1_tarski(D))) )
                  & ( v2_funct_1(E)
                   => ( r2_hidden(D,B)
                      | v2_funct_1(F) ) ) ) ) ) ) ) )).

fof(t69_stirl2_1,axiom,(
    ! [A] :
      ( ( v1_finset_1(A)
        & m1_subset_1(A,k1_zfmisc_1(k5_numbers)) )
     => ? [B] :
          ( v1_funct_1(B)
          & v1_funct_2(B,A,k4_card_1(A))
          & m2_relset_1(B,A,k4_card_1(A))
          & v3_funct_2(B,A,k4_card_1(A))
          & ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ~ ( r2_hidden(C,k4_relset_1(A,k4_card_1(A),B))
                      & r2_hidden(D,k4_relset_1(A,k4_card_1(A),B))
                      & ~ r1_xreal_0(D,C)
                      & r1_xreal_0(k5_stirl2_1(A,k4_card_1(A),B,D),k5_stirl2_1(A,k4_card_1(A),B,C)) ) ) ) ) ) )).

fof(t70_stirl2_1,axiom,(
    ! [A] :
      ( v1_finset_1(A)
     => ! [B] :
          ( v1_finset_1(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,B)
                & m2_relset_1(C,A,B) )
             => ( k4_card_1(A) = k4_card_1(B)
               => ( v2_funct_2(C,A,B)
                <=> v2_funct_1(C) ) ) ) ) ) )).

fof(t71_stirl2_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] :
              ~ ( r2_hidden(C,k2_relat_1(k5_relat_1(A,B)))
                & v2_funct_1(B)
                & ! [D] :
                    ~ ( r2_hidden(D,k1_relat_1(B))
                      & r2_hidden(D,k2_relat_1(A))
                      & k10_relat_1(B,k1_tarski(C)) = k1_tarski(D)
                      & k10_relat_1(A,k1_tarski(D)) = k10_relat_1(k5_relat_1(A,B),k1_tarski(C)) ) ) ) ) )).

fof(d5_stirl2_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k5_numbers))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k5_numbers))
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,B)
                & m2_relset_1(C,A,B) )
             => ( v2_stirl2_1(C,A,B)
              <=> ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ! [E] :
                        ( m2_subset_1(E,k1_numbers,k5_numbers)
                       => ~ ( r2_hidden(D,k5_relset_1(A,B,C))
                            & r2_hidden(E,k5_relset_1(A,B,C))
                            & ~ r1_xreal_0(E,D)
                            & r1_xreal_0(k1_henmodel(k3_funct_2(A,B,C,k1_stirl2_1(E))),k1_henmodel(k3_funct_2(A,B,C,k1_stirl2_1(D)))) ) ) ) ) ) ) ) )).

fof(t72_stirl2_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k5_numbers))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k5_numbers))
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,B)
                & m2_relset_1(C,A,B) )
             => ( v2_stirl2_1(C,A,B)
               => k1_henmodel(k5_relset_1(A,B,C)) = k1_funct_1(C,k1_henmodel(k4_relset_1(A,B,C))) ) ) ) ) )).

fof(t73_stirl2_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k5_numbers))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k5_numbers))
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,B)
                & m2_relset_1(C,A,B) )
             => ~ ( v1_finset_1(k5_relset_1(A,B,C))
                  & ! [D] :
                      ( ( v1_funct_1(D)
                        & v1_funct_2(D,A,B)
                        & m2_relset_1(D,A,B) )
                     => ! [E] :
                          ( ( v1_funct_1(E)
                            & v1_funct_2(E,k5_relset_1(A,B,C),k5_relset_1(A,B,C))
                            & v3_funct_2(E,k5_relset_1(A,B,C),k5_relset_1(A,B,C))
                            & m2_relset_1(E,k5_relset_1(A,B,C),k5_relset_1(A,B,C)) )
                         => ~ ( C = k1_partfun1(A,B,k5_relset_1(A,B,C),k5_relset_1(A,B,C),D,E)
                              & k5_relset_1(A,B,C) = k5_relset_1(A,B,D)
                              & v2_stirl2_1(D,A,B) ) ) ) ) ) ) ) )).

fof(t74_stirl2_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k5_numbers))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k5_numbers))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k5_numbers))
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,B)
                    & m2_relset_1(D,A,B) )
                 => ( v1_finset_1(k5_relset_1(A,B,D))
                   => ! [E] :
                        ( ( v1_funct_1(E)
                          & v1_funct_2(E,A,C)
                          & m2_relset_1(E,A,C) )
                       => ! [F] :
                            ( ( v1_funct_1(F)
                              & v1_funct_2(F,A,C)
                              & m2_relset_1(F,A,C) )
                           => ! [G] :
                                ( ( v1_relat_1(G)
                                  & v1_funct_1(G) )
                               => ! [H] :
                                    ( ( v1_relat_1(H)
                                      & v1_funct_1(H) )
                                   => ( ( v2_funct_1(G)
                                        & v2_funct_1(H)
                                        & k5_relset_1(A,C,E) = k5_relset_1(A,C,F)
                                        & k5_relset_1(A,C,E) = k1_relat_1(G)
                                        & k1_relat_1(G) = k1_relat_1(H)
                                        & D = k5_relat_1(E,G)
                                        & D = k5_relat_1(F,H)
                                        & v2_stirl2_1(E,A,C)
                                        & v2_stirl2_1(F,A,C) )
                                     => ( G = H
                                        & E = F ) ) ) ) ) ) ) ) ) ) ) )).

fof(t75_stirl2_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k5_numbers))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k5_numbers))
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,B)
                & m2_relset_1(C,A,B) )
             => ( v1_finset_1(k5_relset_1(A,B,C))
               => ! [D] :
                    ( ( v1_funct_1(D)
                      & v1_funct_2(D,A,B)
                      & m2_relset_1(D,A,B) )
                   => ! [E] :
                        ( ( v1_funct_1(E)
                          & v1_funct_2(E,A,B)
                          & m2_relset_1(E,A,B) )
                       => ! [F] :
                            ( ( v1_funct_1(F)
                              & v1_funct_2(F,k5_relset_1(A,B,C),k5_relset_1(A,B,C))
                              & v3_funct_2(F,k5_relset_1(A,B,C),k5_relset_1(A,B,C))
                              & m2_relset_1(F,k5_relset_1(A,B,C),k5_relset_1(A,B,C)) )
                           => ! [G] :
                                ( ( v1_funct_1(G)
                                  & v1_funct_2(G,k5_relset_1(A,B,C),k5_relset_1(A,B,C))
                                  & v3_funct_2(G,k5_relset_1(A,B,C),k5_relset_1(A,B,C))
                                  & m2_relset_1(G,k5_relset_1(A,B,C),k5_relset_1(A,B,C)) )
                               => ( ( C = k1_partfun1(A,B,k5_relset_1(A,B,C),k5_relset_1(A,B,C),D,F)
                                    & C = k1_partfun1(A,B,k5_relset_1(A,B,C),k5_relset_1(A,B,C),E,G)
                                    & k5_relset_1(A,B,C) = k5_relset_1(A,B,D)
                                    & k5_relset_1(A,B,C) = k5_relset_1(A,B,E)
                                    & v2_stirl2_1(D,A,B)
                                    & v2_stirl2_1(E,A,B) )
                                 => ( F = G
                                    & D = E ) ) ) ) ) ) ) ) ) ) )).

fof(s2_stirl2_1,axiom,
    ( ( ! [A] :
          ( r2_hidden(A,k4_xboole_0(f3_s2_stirl2_1,f1_s2_stirl2_1))
         => r2_hidden(f6_s2_stirl2_1(A),f4_s2_stirl2_1) )
      & r1_tarski(f1_s2_stirl2_1,f3_s2_stirl2_1)
      & r1_tarski(f2_s2_stirl2_1,f4_s2_stirl2_1)
      & ( v1_xboole_0(f2_s2_stirl2_1)
       => v1_xboole_0(f1_s2_stirl2_1) ) )
   => ? [A] :
        ( v1_funct_1(A)
        & v1_funct_2(A,f3_s2_stirl2_1,f4_s2_stirl2_1)
        & m2_relset_1(A,f3_s2_stirl2_1,f4_s2_stirl2_1)
        & k2_partfun1(f3_s2_stirl2_1,f4_s2_stirl2_1,A,f1_s2_stirl2_1) = f5_s2_stirl2_1
        & ! [B] :
            ( r2_hidden(B,k4_xboole_0(f3_s2_stirl2_1,f1_s2_stirl2_1))
           => k1_funct_1(A,B) = f6_s2_stirl2_1(B) ) ) )).

fof(s5_stirl2_1,axiom,
    ( ( p1_s5_stirl2_1(k4_afinsq_1(f1_s5_stirl2_1))
      & ! [A] :
          ( ( v1_finset_1(A)
            & m1_ordinal1(A,f1_s5_stirl2_1) )
         => ! [B] :
              ( m1_subset_1(B,f1_s5_stirl2_1)
             => ( p1_s5_stirl2_1(A)
               => p1_s5_stirl2_1(k5_afinsq_1(f1_s5_stirl2_1,A,k9_afinsq_1(f1_s5_stirl2_1,B))) ) ) ) )
   => ! [A] :
        ( ( v1_finset_1(A)
          & m1_ordinal1(A,f1_s5_stirl2_1) )
       => p1_s5_stirl2_1(A) ) )).

fof(s6_stirl2_1,axiom,
    ( ! [A] :
        ( m2_subset_1(A,k1_numbers,k5_numbers)
       => ~ ( r2_hidden(A,f2_s6_stirl2_1)
            & ! [B] :
                ( m1_subset_1(B,f1_s6_stirl2_1)
               => ~ p1_s6_stirl2_1(A,B) ) ) )
   => ? [A] :
        ( v1_finset_1(A)
        & m1_ordinal1(A,f1_s6_stirl2_1)
        & k2_afinsq_1(A) = f2_s6_stirl2_1
        & ! [B] :
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => ( r2_hidden(B,f2_s6_stirl2_1)
             => p1_s6_stirl2_1(B,k1_funct_1(A,B)) ) ) ) )).

fof(s7_stirl2_1,axiom,
    ( ( ! [A] :
          ( m2_subset_1(A,k1_numbers,k5_numbers)
         => ( r2_hidden(A,k2_afinsq_1(f2_s7_stirl2_1))
           => v1_finset_1(k1_funct_1(f2_s7_stirl2_1,A)) ) )
      & ! [A] :
          ( m2_subset_1(A,k1_numbers,k5_numbers)
         => ! [B] :
              ( m2_subset_1(B,k1_numbers,k5_numbers)
             => ( ( r2_hidden(A,k2_afinsq_1(f2_s7_stirl2_1))
                  & r2_hidden(B,k2_afinsq_1(f2_s7_stirl2_1)) )
               => ( A = B
                  | r1_xboole_0(k1_funct_1(f2_s7_stirl2_1,A),k1_funct_1(f2_s7_stirl2_1,B)) ) ) ) ) )
   => ? [A] :
        ( v1_finset_1(A)
        & m1_ordinal1(A,k5_numbers)
        & k2_afinsq_1(A) = k2_afinsq_1(f2_s7_stirl2_1)
        & ! [B] :
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => ( r2_hidden(B,k2_afinsq_1(A))
             => k11_stirl2_1(A,B) = k1_card_1(k1_funct_1(f2_s7_stirl2_1,B)) ) )
        & k1_card_1(k3_tarski(k2_relat_1(f2_s7_stirl2_1))) = k10_stirl2_1(A) ) )).

fof(s9_stirl2_1,axiom,
    ( ( p1_s9_stirl2_1(k1_xboole_0)
      & ! [A] :
          ( ( v1_relat_1(A)
            & v1_funct_1(A) )
         => ( ! [B] :
                ( ( r2_hidden(B,k2_relat_1(A))
                  & p2_s9_stirl2_1(B,A) )
               => p1_s9_stirl2_1(k7_relat_1(A,k4_xboole_0(k1_relat_1(A),k10_relat_1(A,k1_tarski(B))))) )
           => p1_s9_stirl2_1(A) ) ) )
   => ! [A] :
        ( ( v1_relat_1(A)
          & v1_funct_1(A) )
       => ( v1_finset_1(k2_relat_1(A))
         => p1_s9_stirl2_1(A) ) ) )).

fof(dt_k1_stirl2_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k5_numbers)
     => m1_subset_1(k1_stirl2_1(A),k1_zfmisc_1(k5_numbers)) ) )).

fof(redefinition_k1_stirl2_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k5_numbers)
     => k1_stirl2_1(A) = k1_tarski(A) ) )).

fof(dt_k2_stirl2_1,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers) )
     => m1_subset_1(k2_stirl2_1(A,B),k1_zfmisc_1(k5_numbers)) ) )).

fof(commutativity_k2_stirl2_1,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers) )
     => k2_stirl2_1(A,B) = k2_stirl2_1(B,A) ) )).

fof(redefinition_k2_stirl2_1,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers) )
     => k2_stirl2_1(A,B) = k2_tarski(A,B) ) )).

fof(dt_k3_stirl2_1,axiom,(
    ! [A,B,C] :
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers)
        & m1_subset_1(C,k5_numbers) )
     => ( ~ v1_xboole_0(k3_stirl2_1(A,B,C))
        & m1_subset_1(k3_stirl2_1(A,B,C),k1_zfmisc_1(k5_numbers)) ) ) )).

fof(redefinition_k3_stirl2_1,axiom,(
    ! [A,B,C] :
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers)
        & m1_subset_1(C,k5_numbers) )
     => k3_stirl2_1(A,B,C) = k1_enumset1(A,B,C) ) )).

fof(dt_k4_stirl2_1,axiom,(
    ! [A,B,C,D] :
      ( ( m1_subset_1(A,k5_numbers)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B) )
     => m1_subset_1(k4_stirl2_1(A,B,C,D),k1_zfmisc_1(k5_numbers)) ) )).

fof(redefinition_k4_stirl2_1,axiom,(
    ! [A,B,C,D] :
      ( ( m1_subset_1(A,k5_numbers)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B) )
     => k4_stirl2_1(A,B,C,D) = k10_relat_1(C,D) ) )).

fof(dt_k5_stirl2_1,axiom,(
    ! [A,B,C,D] :
      ( ( m1_subset_1(B,k5_numbers)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B) )
     => m1_subset_1(k5_stirl2_1(A,B,C,D),B) ) )).

fof(redefinition_k5_stirl2_1,axiom,(
    ! [A,B,C,D] :
      ( ( m1_subset_1(B,k5_numbers)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B) )
     => k5_stirl2_1(A,B,C,D) = k1_funct_1(C,D) ) )).

fof(dt_k6_stirl2_1,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers) )
     => m2_subset_1(k6_stirl2_1(A,B),k1_numbers,k5_numbers) ) )).

fof(dt_k7_stirl2_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & v1_finset_1(B)
        & m1_ordinal1(B,A)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(A,A),A)
        & m1_relset_1(C,k2_zfmisc_1(A,A),A) )
     => m1_subset_1(k7_stirl2_1(A,B,C),A) ) )).

fof(dt_k8_stirl2_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A)
        & m1_subset_1(C,A) )
     => ( v1_finset_1(k8_stirl2_1(A,B,C))
        & m1_ordinal1(k8_stirl2_1(A,B,C),A) ) ) )).

fof(redefinition_k8_stirl2_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A)
        & m1_subset_1(C,A) )
     => k8_stirl2_1(A,B,C) = k7_afinsq_1(B,C) ) )).

fof(dt_k9_stirl2_1,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A)
        & m1_subset_1(C,A)
        & m1_subset_1(D,A) )
     => ( v1_finset_1(k9_stirl2_1(A,B,C,D))
        & m1_ordinal1(k9_stirl2_1(A,B,C,D),A) ) ) )).

fof(redefinition_k9_stirl2_1,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A)
        & m1_subset_1(C,A)
        & m1_subset_1(D,A) )
     => k9_stirl2_1(A,B,C,D) = k8_afinsq_1(B,C,D) ) )).

fof(dt_k10_stirl2_1,axiom,(
    ! [A] :
      ( ( v1_finset_1(A)
        & m1_ordinal1(A,k5_numbers) )
     => m2_subset_1(k10_stirl2_1(A),k1_numbers,k5_numbers) ) )).

fof(dt_k11_stirl2_1,axiom,(
    ! [A,B] :
      ( ( v1_finset_1(A)
        & m1_ordinal1(A,k5_numbers) )
     => m2_subset_1(k11_stirl2_1(A,B),k1_numbers,k5_numbers) ) )).

fof(redefinition_k11_stirl2_1,axiom,(
    ! [A,B] :
      ( ( v1_finset_1(A)
        & m1_ordinal1(A,k5_numbers) )
     => k11_stirl2_1(A,B) = k1_funct_1(A,B) ) )).

fof(t24_stirl2_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => v1_finset_1(a_2_0_stirl2_1(A,B)) ) ) )).

fof(t25_stirl2_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => m2_subset_1(k1_card_1(a_2_0_stirl2_1(A,B)),k1_numbers,k5_numbers) ) ) )).

fof(d2_stirl2_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => k6_stirl2_1(A,B) = k1_card_1(a_2_0_stirl2_1(A,B)) ) ) )).

fof(t42_stirl2_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => k1_card_1(a_2_1_stirl2_1(A,B)) = k1_card_1(a_2_0_stirl2_1(A,B)) ) ) )).

fof(t43_stirl2_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( ~ r1_xreal_0(A,C)
               => k1_card_1(a_3_0_stirl2_1(A,B,C)) = k1_card_1(a_2_2_stirl2_1(A,B)) ) ) ) ) )).

fof(t55_stirl2_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => k24_binop_2(A,k6_stirl2_1(B,A)) = k1_card_1(a_2_3_stirl2_1(A,B)) ) ) )).

fof(s1_stirl2_1,axiom,(
    v1_finset_1(a_0_0_stirl2_1) )).

fof(s3_stirl2_1,axiom,
    ( ( ! [A] :
          ( r2_hidden(A,k4_xboole_0(f3_s3_stirl2_1,f1_s3_stirl2_1))
         => r2_hidden(f5_s3_stirl2_1(A),f4_s3_stirl2_1) )
      & r1_tarski(f1_s3_stirl2_1,f3_s3_stirl2_1)
      & r1_tarski(f2_s3_stirl2_1,f4_s3_stirl2_1)
      & ( v1_xboole_0(f2_s3_stirl2_1)
       => v1_xboole_0(f1_s3_stirl2_1) )
      & ! [A] :
          ( ( v1_funct_1(A)
            & v1_funct_2(A,f3_s3_stirl2_1,f4_s3_stirl2_1)
            & m2_relset_1(A,f3_s3_stirl2_1,f4_s3_stirl2_1) )
         => ( ! [B] :
                ( r2_hidden(B,k4_xboole_0(f3_s3_stirl2_1,f1_s3_stirl2_1))
               => f5_s3_stirl2_1(B) = k1_funct_1(A,B) )
           => ( p1_s3_stirl2_1(A,f3_s3_stirl2_1,f4_s3_stirl2_1)
            <=> p1_s3_stirl2_1(k2_partfun1(f3_s3_stirl2_1,f4_s3_stirl2_1,A,f1_s3_stirl2_1),f1_s3_stirl2_1,f2_s3_stirl2_1) ) ) ) )
   => k1_card_1(a_0_1_stirl2_1) = k1_card_1(a_0_2_stirl2_1) )).

fof(s4_stirl2_1,axiom,
    ( ( ( v1_xboole_0(f2_s4_stirl2_1)
       => v1_xboole_0(f1_s4_stirl2_1) )
      & ~ r2_hidden(f3_s4_stirl2_1,f1_s4_stirl2_1)
      & ! [A] :
          ( ( v1_funct_1(A)
            & v1_funct_2(A,k2_xboole_0(f1_s4_stirl2_1,k1_tarski(f3_s4_stirl2_1)),k2_xboole_0(f2_s4_stirl2_1,k1_tarski(f4_s4_stirl2_1)))
            & m2_relset_1(A,k2_xboole_0(f1_s4_stirl2_1,k1_tarski(f3_s4_stirl2_1)),k2_xboole_0(f2_s4_stirl2_1,k1_tarski(f4_s4_stirl2_1))) )
         => ( k1_funct_1(A,f3_s4_stirl2_1) = f4_s4_stirl2_1
           => ( p1_s4_stirl2_1(A,k2_xboole_0(f1_s4_stirl2_1,k1_tarski(f3_s4_stirl2_1)),k2_xboole_0(f2_s4_stirl2_1,k1_tarski(f4_s4_stirl2_1)))
            <=> p1_s4_stirl2_1(k2_partfun1(k2_xboole_0(f1_s4_stirl2_1,k1_tarski(f3_s4_stirl2_1)),k2_xboole_0(f2_s4_stirl2_1,k1_tarski(f4_s4_stirl2_1)),A,f1_s4_stirl2_1),f1_s4_stirl2_1,f2_s4_stirl2_1) ) ) ) )
   => k1_card_1(a_0_3_stirl2_1) = k1_card_1(a_0_4_stirl2_1) )).

fof(s8_stirl2_1,axiom,
    ( ( v2_funct_2(f4_s8_stirl2_1,k4_card_1(f2_s8_stirl2_1),f2_s8_stirl2_1)
      & v2_funct_1(f4_s8_stirl2_1)
      & ~ v1_xboole_0(f2_s8_stirl2_1)
      & r2_hidden(f3_s8_stirl2_1,f1_s8_stirl2_1) )
   => ? [A] :
        ( v1_finset_1(A)
        & m1_ordinal1(A,k5_numbers)
        & k2_afinsq_1(A) = k4_card_1(f2_s8_stirl2_1)
        & k1_card_1(a_0_5_stirl2_1) = k10_stirl2_1(A)
        & ! [B] :
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => ( r2_hidden(B,k2_afinsq_1(A))
             => k11_stirl2_1(A,B) = k1_card_1(a_1_0_stirl2_1(B)) ) ) ) )).

fof(fraenkel_a_2_0_stirl2_1,axiom,(
    ! [A,B,C] :
      ( ( m2_subset_1(B,k1_numbers,k5_numbers)
        & m2_subset_1(C,k1_numbers,k5_numbers) )
     => ( r2_hidden(A,a_2_0_stirl2_1(B,C))
      <=> ? [D] :
            ( v1_funct_1(D)
            & v1_funct_2(D,B,C)
            & m2_relset_1(D,B,C)
            & A = D
            & v2_funct_2(D,B,C)
            & v1_stirl2_1(D,B,C) ) ) ) )).

fof(fraenkel_a_2_1_stirl2_1,axiom,(
    ! [A,B,C] :
      ( ( m2_subset_1(B,k1_numbers,k5_numbers)
        & m2_subset_1(C,k1_numbers,k5_numbers) )
     => ( r2_hidden(A,a_2_1_stirl2_1(B,C))
      <=> ? [D] :
            ( v1_funct_1(D)
            & v1_funct_2(D,k23_binop_2(B,np__1),k23_binop_2(C,np__1))
            & m2_relset_1(D,k23_binop_2(B,np__1),k23_binop_2(C,np__1))
            & A = D
            & v2_funct_2(D,k23_binop_2(B,np__1),k23_binop_2(C,np__1))
            & v1_stirl2_1(D,k23_binop_2(B,np__1),k23_binop_2(C,np__1))
            & k4_stirl2_1(k23_binop_2(B,np__1),k23_binop_2(C,np__1),D,k2_setwiseo(k23_binop_2(C,np__1),k5_stirl2_1(k23_binop_2(B,np__1),k23_binop_2(C,np__1),D,B))) = k1_stirl2_1(B) ) ) ) )).

fof(fraenkel_a_3_0_stirl2_1,axiom,(
    ! [A,B,C,D] :
      ( ( m2_subset_1(B,k1_numbers,k5_numbers)
        & m2_subset_1(C,k1_numbers,k5_numbers)
        & m2_subset_1(D,k1_numbers,k5_numbers) )
     => ( r2_hidden(A,a_3_0_stirl2_1(B,C,D))
      <=> ? [E] :
            ( v1_funct_1(E)
            & v1_funct_2(E,k23_binop_2(C,np__1),B)
            & m2_relset_1(E,k23_binop_2(C,np__1),B)
            & A = E
            & v2_funct_2(E,k23_binop_2(C,np__1),B)
            & v1_stirl2_1(E,k23_binop_2(C,np__1),B)
            & k4_stirl2_1(k23_binop_2(C,np__1),B,E,k1_tarski(k5_stirl2_1(k23_binop_2(C,np__1),B,E,C))) != k1_stirl2_1(C)
            & k5_stirl2_1(k23_binop_2(C,np__1),B,E,C) = D ) ) ) )).

fof(fraenkel_a_2_2_stirl2_1,axiom,(
    ! [A,B,C] :
      ( ( m2_subset_1(B,k1_numbers,k5_numbers)
        & m2_subset_1(C,k1_numbers,k5_numbers) )
     => ( r2_hidden(A,a_2_2_stirl2_1(B,C))
      <=> ? [D] :
            ( v1_funct_1(D)
            & v1_funct_2(D,C,B)
            & m2_relset_1(D,C,B)
            & A = D
            & v2_funct_2(D,C,B)
            & v1_stirl2_1(D,C,B) ) ) ) )).

fof(fraenkel_a_2_3_stirl2_1,axiom,(
    ! [A,B,C] :
      ( ( m2_subset_1(B,k1_numbers,k5_numbers)
        & m2_subset_1(C,k1_numbers,k5_numbers) )
     => ( r2_hidden(A,a_2_3_stirl2_1(B,C))
      <=> ? [D] :
            ( v1_funct_1(D)
            & v1_funct_2(D,k23_binop_2(C,np__1),B)
            & m2_relset_1(D,k23_binop_2(C,np__1),B)
            & A = D
            & v2_funct_2(D,k23_binop_2(C,np__1),B)
            & v1_stirl2_1(D,k23_binop_2(C,np__1),B)
            & k4_stirl2_1(k23_binop_2(C,np__1),B,D,k1_tarski(k5_stirl2_1(k23_binop_2(C,np__1),B,D,C))) != k1_stirl2_1(C) ) ) ) )).

fof(fraenkel_a_0_0_stirl2_1,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_0_stirl2_1)
    <=> ? [B] :
          ( v1_funct_1(B)
          & v1_funct_2(B,f1_s1_stirl2_1,f2_s1_stirl2_1)
          & m2_relset_1(B,f1_s1_stirl2_1,f2_s1_stirl2_1)
          & A = B
          & p1_s1_stirl2_1(B) ) ) )).

fof(fraenkel_a_0_1_stirl2_1,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_1_stirl2_1)
    <=> ? [B] :
          ( v1_funct_1(B)
          & v1_funct_2(B,f1_s3_stirl2_1,f2_s3_stirl2_1)
          & m2_relset_1(B,f1_s3_stirl2_1,f2_s3_stirl2_1)
          & A = B
          & p1_s3_stirl2_1(B,f1_s3_stirl2_1,f2_s3_stirl2_1) ) ) )).

fof(fraenkel_a_0_2_stirl2_1,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_2_stirl2_1)
    <=> ? [B] :
          ( v1_funct_1(B)
          & v1_funct_2(B,f3_s3_stirl2_1,f4_s3_stirl2_1)
          & m2_relset_1(B,f3_s3_stirl2_1,f4_s3_stirl2_1)
          & A = B
          & p1_s3_stirl2_1(B,f3_s3_stirl2_1,f4_s3_stirl2_1)
          & r1_tarski(k5_relset_1(f3_s3_stirl2_1,f4_s3_stirl2_1,k2_partfun1(f3_s3_stirl2_1,f4_s3_stirl2_1,B,f1_s3_stirl2_1)),f2_s3_stirl2_1)
          & ! [C] :
              ( r2_hidden(C,k4_xboole_0(f3_s3_stirl2_1,f1_s3_stirl2_1))
             => k1_funct_1(B,C) = f5_s3_stirl2_1(C) ) ) ) )).

fof(fraenkel_a_0_3_stirl2_1,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_3_stirl2_1)
    <=> ? [B] :
          ( v1_funct_1(B)
          & v1_funct_2(B,f1_s4_stirl2_1,f2_s4_stirl2_1)
          & m2_relset_1(B,f1_s4_stirl2_1,f2_s4_stirl2_1)
          & A = B
          & p1_s4_stirl2_1(B,f1_s4_stirl2_1,f2_s4_stirl2_1) ) ) )).

fof(fraenkel_a_0_4_stirl2_1,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_4_stirl2_1)
    <=> ? [B] :
          ( v1_funct_1(B)
          & v1_funct_2(B,k2_xboole_0(f1_s4_stirl2_1,k1_tarski(f3_s4_stirl2_1)),k2_xboole_0(f2_s4_stirl2_1,k1_tarski(f4_s4_stirl2_1)))
          & m2_relset_1(B,k2_xboole_0(f1_s4_stirl2_1,k1_tarski(f3_s4_stirl2_1)),k2_xboole_0(f2_s4_stirl2_1,k1_tarski(f4_s4_stirl2_1)))
          & A = B
          & p1_s4_stirl2_1(B,k2_xboole_0(f1_s4_stirl2_1,k1_tarski(f3_s4_stirl2_1)),k2_xboole_0(f2_s4_stirl2_1,k1_tarski(f4_s4_stirl2_1)))
          & r1_tarski(k5_relset_1(k2_xboole_0(f1_s4_stirl2_1,k1_tarski(f3_s4_stirl2_1)),k2_xboole_0(f2_s4_stirl2_1,k1_tarski(f4_s4_stirl2_1)),k2_partfun1(k2_xboole_0(f1_s4_stirl2_1,k1_tarski(f3_s4_stirl2_1)),k2_xboole_0(f2_s4_stirl2_1,k1_tarski(f4_s4_stirl2_1)),B,f1_s4_stirl2_1)),f2_s4_stirl2_1)
          & k1_funct_1(B,f3_s4_stirl2_1) = f4_s4_stirl2_1 ) ) )).

fof(fraenkel_a_0_5_stirl2_1,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_5_stirl2_1)
    <=> ? [B] :
          ( v1_funct_1(B)
          & v1_funct_2(B,f1_s8_stirl2_1,f2_s8_stirl2_1)
          & m2_relset_1(B,f1_s8_stirl2_1,f2_s8_stirl2_1)
          & A = B
          & p1_s8_stirl2_1(B) ) ) )).

fof(fraenkel_a_1_0_stirl2_1,axiom,(
    ! [A,B] :
      ( m2_subset_1(B,k1_numbers,k5_numbers)
     => ( r2_hidden(A,a_1_0_stirl2_1(B))
      <=> ? [C] :
            ( v1_funct_1(C)
            & v1_funct_2(C,f1_s8_stirl2_1,f2_s8_stirl2_1)
            & m2_relset_1(C,f1_s8_stirl2_1,f2_s8_stirl2_1)
            & A = C
            & p1_s8_stirl2_1(C)
            & k1_funct_1(C,f3_s8_stirl2_1) = k1_funct_1(f4_s8_stirl2_1,B) ) ) ) )).
%------------------------------------------------------------------------------