SET007 Axioms: SET007+262.ax


%------------------------------------------------------------------------------
% File     : SET007+262 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Several Properties of Fields. Field Theory
% 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    : realset3 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   47 (   6 unit)
%            Number of atoms       :  242 (  50 equality)
%            Maximal formula depth :   12 (   7 average)
%            Number of connectives :  195 (   0 ~  ;   1  |;  50  &)
%                                         (  11 <=>; 133 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :    8 (   1 propositional; 0-3 arity)
%            Number of functors    :   16 (   0 constant; 1-6 arity)
%            Number of variables   :  133 (   0 singleton; 133 !;   0 ?)
%            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(t1_realset3,axiom,(
    ! [A] :
      ( ( v4_realset2(A)
        & l3_vectsp_1(A) )
     => k8_funct_2(k2_realset2(A),k2_realset2(A),k7_realset2(A),k4_realset2(A)) = k4_realset2(A) ) )).

fof(t2_realset3,axiom,(
    ! [A] :
      ( ( v4_realset2(A)
        & l3_vectsp_1(A) )
     => k8_funct_2(k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))),k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))),k8_realset2(A),k6_realset2(A)) = k6_realset2(A) ) )).

fof(t3_realset3,axiom,(
    ! [A] :
      ( ( v4_realset2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k2_realset2(A))
         => ! [C] :
              ( m1_subset_1(C,k2_realset2(A))
             => k1_funct_1(k7_realset2(A),k1_funct_1(k3_realset2(A),k4_tarski(B,k8_funct_2(k2_realset2(A),k2_realset2(A),k7_realset2(A),C)))) = k1_funct_1(k3_realset2(A),k4_tarski(C,k8_funct_2(k2_realset2(A),k2_realset2(A),k7_realset2(A),B))) ) ) ) )).

fof(t4_realset3,axiom,(
    ! [A] :
      ( ( v4_realset2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))))
         => ! [C] :
              ( m1_subset_1(C,k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))))
             => k1_funct_1(k8_realset2(A),k1_funct_1(k5_realset2(A),k4_tarski(B,k8_funct_2(k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))),k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))),k8_realset2(A),C)))) = k1_funct_1(k5_realset2(A),k4_tarski(C,k8_funct_2(k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))),k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))),k8_realset2(A),B))) ) ) ) )).

fof(t5_realset3,axiom,(
    ! [A] :
      ( ( v4_realset2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k2_realset2(A))
         => ! [C] :
              ( m1_subset_1(C,k2_realset2(A))
             => k1_funct_1(k7_realset2(A),k1_funct_1(k3_realset2(A),k4_tarski(B,C))) = k2_binop_1(k2_realset2(A),k2_realset2(A),k2_realset2(A),k3_realset2(A),k8_funct_2(k2_realset2(A),k2_realset2(A),k7_realset2(A),B),k8_funct_2(k2_realset2(A),k2_realset2(A),k7_realset2(A),C)) ) ) ) )).

fof(t6_realset3,axiom,(
    ! [A] :
      ( ( v4_realset2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))))
         => ! [C] :
              ( m1_subset_1(C,k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))))
             => k1_funct_1(k8_realset2(A),k1_funct_1(k5_realset2(A),k4_tarski(B,C))) = k1_funct_1(k5_realset2(A),k4_tarski(k8_funct_2(k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))),k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))),k8_realset2(A),B),k8_funct_2(k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))),k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))),k8_realset2(A),C))) ) ) ) )).

fof(t7_realset3,axiom,(
    ! [A] :
      ( ( v4_realset2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k2_realset2(A))
         => ! [C] :
              ( m1_subset_1(C,k2_realset2(A))
             => ! [D] :
                  ( m1_subset_1(D,k2_realset2(A))
                 => ! [E] :
                      ( m1_subset_1(E,k2_realset2(A))
                     => ( k2_binop_1(k2_realset2(A),k2_realset2(A),k2_realset2(A),k3_realset2(A),B,k8_funct_2(k2_realset2(A),k2_realset2(A),k7_realset2(A),C)) = k1_funct_1(k3_realset2(A),k4_tarski(D,k8_funct_2(k2_realset2(A),k2_realset2(A),k7_realset2(A),E)))
                      <=> k1_funct_1(k3_realset2(A),k4_tarski(B,E)) = k1_funct_1(k3_realset2(A),k4_tarski(C,D)) ) ) ) ) ) ) )).

fof(t8_realset3,axiom,(
    ! [A] :
      ( ( v4_realset2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k2_realset2(A))
         => ! [C] :
              ( m1_subset_1(C,k2_realset2(A))
             => ! [D] :
                  ( m1_subset_1(D,k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))))
                 => ! [E] :
                      ( m1_subset_1(E,k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))))
                     => ( k1_funct_1(k5_realset2(A),k4_tarski(B,k8_funct_2(k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))),k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))),k8_realset2(A),D))) = k1_funct_1(k5_realset2(A),k4_tarski(C,k8_funct_2(k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))),k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))),k8_realset2(A),E)))
                      <=> k1_funct_1(k5_realset2(A),k4_tarski(B,E)) = k1_funct_1(k5_realset2(A),k4_tarski(D,C)) ) ) ) ) ) ) )).

fof(t9_realset3,axiom,(
    ! [A] :
      ( ( v4_realset2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k2_realset2(A))
         => ! [C] :
              ( m1_subset_1(C,k2_realset2(A))
             => ( k1_funct_1(k5_realset2(A),k4_tarski(B,C)) = k4_realset2(A)
              <=> ( B = k4_realset2(A)
                  | C = k4_realset2(A) ) ) ) ) ) )).

fof(t10_realset3,axiom,(
    ! [A] :
      ( ( v4_realset2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k2_realset2(A))
         => ! [C] :
              ( m1_subset_1(C,k2_realset2(A))
             => ! [D] :
                  ( m1_subset_1(D,k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))))
                 => ! [E] :
                      ( m1_subset_1(E,k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))))
                     => k1_funct_1(k5_realset2(A),k4_tarski(k1_funct_1(k5_realset2(A),k4_tarski(B,k8_funct_2(k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))),k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))),k8_realset2(A),D))),k1_funct_1(k5_realset2(A),k4_tarski(C,k8_funct_2(k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))),k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))),k8_realset2(A),E))))) = k1_funct_1(k5_realset2(A),k4_tarski(k1_funct_1(k5_realset2(A),k4_tarski(B,C)),k1_funct_1(k8_realset2(A),k1_funct_1(k5_realset2(A),k4_tarski(D,E))))) ) ) ) ) ) )).

fof(t11_realset3,axiom,(
    ! [A] :
      ( ( v4_realset2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k2_realset2(A))
         => ! [C] :
              ( m1_subset_1(C,k2_realset2(A))
             => ! [D] :
                  ( m1_subset_1(D,k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))))
                 => ! [E] :
                      ( m1_subset_1(E,k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))))
                     => k1_funct_1(k3_realset2(A),k4_tarski(k1_funct_1(k5_realset2(A),k4_tarski(B,k8_funct_2(k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))),k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))),k8_realset2(A),D))),k1_funct_1(k5_realset2(A),k4_tarski(C,k8_funct_2(k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))),k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))),k8_realset2(A),E))))) = k1_funct_1(k5_realset2(A),k4_tarski(k1_funct_1(k3_realset2(A),k4_tarski(k1_funct_1(k5_realset2(A),k4_tarski(B,E)),k1_funct_1(k5_realset2(A),k4_tarski(C,D)))),k1_funct_1(k8_realset2(A),k1_funct_1(k5_realset2(A),k4_tarski(D,E))))) ) ) ) ) ) )).

fof(d1_realset3,axiom,(
    ! [A] :
      ( ( v4_realset2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k2_zfmisc_1(k2_realset2(A),k2_realset2(A)),k2_realset2(A))
            & m2_relset_1(B,k2_zfmisc_1(k2_realset2(A),k2_realset2(A)),k2_realset2(A)) )
         => ( B = k1_realset3(A)
          <=> ! [C] :
                ( m1_subset_1(C,k2_realset2(A))
               => ! [D] :
                    ( m1_subset_1(D,k2_realset2(A))
                   => k1_funct_1(B,k4_tarski(C,D)) = k1_funct_1(k3_realset2(A),k4_tarski(C,k8_funct_2(k2_realset2(A),k2_realset2(A),k7_realset2(A),D))) ) ) ) ) ) )).

fof(t12_realset3,axiom,(
    $true )).

fof(t13_realset3,axiom,(
    $true )).

fof(t14_realset3,axiom,(
    ! [A] :
      ( ( v4_realset2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k2_realset2(A))
         => k1_funct_1(k1_realset3(A),k4_tarski(B,B)) = k4_realset2(A) ) ) )).

fof(t15_realset3,axiom,(
    ! [A] :
      ( ( v4_realset2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k2_realset2(A))
         => ! [C] :
              ( m1_subset_1(C,k2_realset2(A))
             => ! [D] :
                  ( m1_subset_1(D,k2_realset2(A))
                 => k1_funct_1(k5_realset2(A),k4_tarski(B,k1_funct_1(k1_realset3(A),k4_tarski(C,D)))) = k1_funct_1(k1_realset3(A),k4_tarski(k1_funct_1(k5_realset2(A),k4_tarski(B,C)),k1_funct_1(k5_realset2(A),k4_tarski(B,D)))) ) ) ) ) )).

fof(t16_realset3,axiom,(
    ! [A] :
      ( ( v4_realset2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k2_realset2(A))
         => ! [C] :
              ( m1_subset_1(C,k2_realset2(A))
             => m1_subset_1(k1_funct_1(k1_realset3(A),k4_tarski(B,C)),k2_realset2(A)) ) ) ) )).

fof(t17_realset3,axiom,(
    ! [A] :
      ( ( v4_realset2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k2_realset2(A))
         => ! [C] :
              ( m1_subset_1(C,k2_realset2(A))
             => ! [D] :
                  ( m1_subset_1(D,k2_realset2(A))
                 => k1_funct_1(k5_realset2(A),k4_tarski(k1_funct_1(k1_realset3(A),k4_tarski(B,C)),D)) = k1_funct_1(k1_realset3(A),k4_tarski(k1_funct_1(k5_realset2(A),k4_tarski(B,D)),k1_funct_1(k5_realset2(A),k4_tarski(C,D)))) ) ) ) ) )).

fof(t18_realset3,axiom,(
    ! [A] :
      ( ( v4_realset2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k2_realset2(A))
         => ! [C] :
              ( m1_subset_1(C,k2_realset2(A))
             => k1_funct_1(k1_realset3(A),k4_tarski(B,C)) = k1_funct_1(k7_realset2(A),k1_funct_1(k1_realset3(A),k4_tarski(C,B))) ) ) ) )).

fof(t19_realset3,axiom,(
    ! [A] :
      ( ( v4_realset2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k2_realset2(A))
         => ! [C] :
              ( m1_subset_1(C,k2_realset2(A))
             => k1_funct_1(k1_realset3(A),k4_tarski(k8_funct_2(k2_realset2(A),k2_realset2(A),k7_realset2(A),B),C)) = k8_funct_2(k2_realset2(A),k2_realset2(A),k7_realset2(A),k2_binop_1(k2_realset2(A),k2_realset2(A),k2_realset2(A),k3_realset2(A),B,C)) ) ) ) )).

fof(t20_realset3,axiom,(
    ! [A] :
      ( ( v4_realset2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k2_realset2(A))
         => ! [C] :
              ( m1_subset_1(C,k2_realset2(A))
             => ! [D] :
                  ( m1_subset_1(D,k2_realset2(A))
                 => ! [E] :
                      ( m1_subset_1(E,k2_realset2(A))
                     => ( k1_funct_1(k1_realset3(A),k4_tarski(B,C)) = k1_funct_1(k1_realset3(A),k4_tarski(D,E))
                      <=> k1_funct_1(k3_realset2(A),k4_tarski(B,E)) = k1_funct_1(k3_realset2(A),k4_tarski(C,D)) ) ) ) ) ) ) )).

fof(t21_realset3,axiom,(
    ! [A] :
      ( ( v4_realset2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k2_realset2(A))
         => k1_funct_1(k1_realset3(A),k4_tarski(k4_realset2(A),B)) = k8_funct_2(k2_realset2(A),k2_realset2(A),k7_realset2(A),B) ) ) )).

fof(t22_realset3,axiom,(
    ! [A] :
      ( ( v4_realset2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k2_realset2(A))
         => k1_funct_1(k1_realset3(A),k4_tarski(B,k4_realset2(A))) = B ) ) )).

fof(t23_realset3,axiom,(
    ! [A] :
      ( ( v4_realset2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k2_realset2(A))
         => ! [C] :
              ( m1_subset_1(C,k2_realset2(A))
             => ! [D] :
                  ( m1_subset_1(D,k2_realset2(A))
                 => ( k1_funct_1(k3_realset2(A),k4_tarski(B,C)) = D
                  <=> k1_funct_1(k1_realset3(A),k4_tarski(D,B)) = C ) ) ) ) ) )).

fof(t24_realset3,axiom,(
    ! [A] :
      ( ( v4_realset2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k2_realset2(A))
         => ! [C] :
              ( m1_subset_1(C,k2_realset2(A))
             => ! [D] :
                  ( m1_subset_1(D,k2_realset2(A))
                 => ( k1_funct_1(k3_realset2(A),k4_tarski(B,C)) = D
                  <=> k1_funct_1(k1_realset3(A),k4_tarski(D,C)) = B ) ) ) ) ) )).

fof(t25_realset3,axiom,(
    ! [A] :
      ( ( v4_realset2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k2_realset2(A))
         => ! [C] :
              ( m1_subset_1(C,k2_realset2(A))
             => ! [D] :
                  ( m1_subset_1(D,k2_realset2(A))
                 => k1_funct_1(k1_realset3(A),k4_tarski(B,k1_funct_1(k1_realset3(A),k4_tarski(C,D)))) = k1_funct_1(k3_realset2(A),k4_tarski(k1_funct_1(k1_realset3(A),k4_tarski(B,C)),D)) ) ) ) ) )).

fof(t26_realset3,axiom,(
    ! [A] :
      ( ( v4_realset2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k2_realset2(A))
         => ! [C] :
              ( m1_subset_1(C,k2_realset2(A))
             => ! [D] :
                  ( m1_subset_1(D,k2_realset2(A))
                 => k1_funct_1(k1_realset3(A),k4_tarski(B,k1_funct_1(k3_realset2(A),k4_tarski(C,D)))) = k1_funct_1(k1_realset3(A),k4_tarski(k1_funct_1(k1_realset3(A),k4_tarski(B,C)),D)) ) ) ) ) )).

fof(d2_realset3,axiom,(
    ! [A] :
      ( ( v4_realset2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k2_zfmisc_1(k2_realset2(A),k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A)))),k2_realset2(A))
            & m2_relset_1(B,k2_zfmisc_1(k2_realset2(A),k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A)))),k2_realset2(A)) )
         => ( B = k2_realset3(A)
          <=> ! [C] :
                ( m1_subset_1(C,k2_realset2(A))
               => ! [D] :
                    ( m1_subset_1(D,k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))))
                   => k1_funct_1(B,k4_tarski(C,D)) = k1_funct_1(k5_realset2(A),k4_tarski(C,k8_funct_2(k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))),k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))),k8_realset2(A),D))) ) ) ) ) ) )).

fof(t27_realset3,axiom,(
    $true )).

fof(t28_realset3,axiom,(
    $true )).

fof(t29_realset3,axiom,(
    ! [A] :
      ( ( v4_realset2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))))
         => k1_funct_1(k2_realset3(A),k4_tarski(B,B)) = k6_realset2(A) ) ) )).

fof(t30_realset3,axiom,(
    ! [A] :
      ( ( v4_realset2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k2_realset2(A))
         => ! [C] :
              ( m1_subset_1(C,k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))))
             => m1_subset_1(k1_funct_1(k2_realset3(A),k4_tarski(B,C)),k2_realset2(A)) ) ) ) )).

fof(t31_realset3,axiom,(
    ! [A] :
      ( ( v4_realset2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k2_realset2(A))
         => ! [C] :
              ( m1_subset_1(C,k2_realset2(A))
             => ! [D] :
                  ( m1_subset_1(D,k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))))
                 => k1_funct_1(k5_realset2(A),k4_tarski(B,k1_funct_1(k2_realset3(A),k4_tarski(C,D)))) = k1_funct_1(k2_realset3(A),k4_tarski(k1_funct_1(k5_realset2(A),k4_tarski(B,C)),D)) ) ) ) ) )).

fof(t32_realset3,axiom,(
    ! [A] :
      ( ( v4_realset2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))))
         => ( k1_funct_1(k5_realset2(A),k4_tarski(B,k1_funct_1(k2_realset3(A),k4_tarski(k6_realset2(A),B)))) = k6_realset2(A)
            & k1_funct_1(k5_realset2(A),k4_tarski(k1_funct_1(k2_realset3(A),k4_tarski(k6_realset2(A),B)),B)) = k6_realset2(A) ) ) ) )).

fof(t33_realset3,axiom,(
    $true )).

fof(t34_realset3,axiom,(
    $true )).

fof(t35_realset3,axiom,(
    ! [A] :
      ( ( v4_realset2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))))
         => ! [C] :
              ( m1_subset_1(C,k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))))
             => k1_funct_1(k2_realset3(A),k4_tarski(B,C)) = k1_funct_1(k8_realset2(A),k1_funct_1(k2_realset3(A),k4_tarski(C,B))) ) ) ) )).

fof(t36_realset3,axiom,(
    ! [A] :
      ( ( v4_realset2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))))
         => ! [C] :
              ( m1_subset_1(C,k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))))
             => k1_funct_1(k2_realset3(A),k4_tarski(k8_funct_2(k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))),k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))),k8_realset2(A),B),C)) = k1_funct_1(k8_realset2(A),k1_funct_1(k5_realset2(A),k4_tarski(B,C))) ) ) ) )).

fof(t37_realset3,axiom,(
    ! [A] :
      ( ( v4_realset2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k2_realset2(A))
         => ! [C] :
              ( m1_subset_1(C,k2_realset2(A))
             => ! [D] :
                  ( m1_subset_1(D,k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))))
                 => ! [E] :
                      ( m1_subset_1(E,k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))))
                     => ( k1_funct_1(k2_realset3(A),k4_tarski(B,D)) = k1_funct_1(k2_realset3(A),k4_tarski(C,E))
                      <=> k1_funct_1(k5_realset2(A),k4_tarski(B,E)) = k1_funct_1(k5_realset2(A),k4_tarski(D,C)) ) ) ) ) ) ) )).

fof(t38_realset3,axiom,(
    ! [A] :
      ( ( v4_realset2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))))
         => k1_funct_1(k2_realset3(A),k4_tarski(k6_realset2(A),B)) = k8_funct_2(k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))),k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))),k8_realset2(A),B) ) ) )).

fof(t39_realset3,axiom,(
    ! [A] :
      ( ( v4_realset2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k2_realset2(A))
         => k1_funct_1(k2_realset3(A),k4_tarski(B,k6_realset2(A))) = B ) ) )).

fof(t40_realset3,axiom,(
    ! [A] :
      ( ( v4_realset2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))))
         => ! [C] :
              ( m1_subset_1(C,k2_realset2(A))
             => ! [D] :
                  ( m1_subset_1(D,k2_realset2(A))
                 => ( k1_funct_1(k5_realset2(A),k4_tarski(B,C)) = D
                  <=> k1_funct_1(k2_realset3(A),k4_tarski(D,B)) = C ) ) ) ) ) )).

fof(t41_realset3,axiom,(
    ! [A] :
      ( ( v4_realset2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k2_realset2(A))
         => ! [C] :
              ( m1_subset_1(C,k2_realset2(A))
             => ! [D] :
                  ( m1_subset_1(D,k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))))
                 => ( k1_funct_1(k5_realset2(A),k4_tarski(B,D)) = C
                  <=> k1_funct_1(k2_realset3(A),k4_tarski(C,D)) = B ) ) ) ) ) )).

fof(t42_realset3,axiom,(
    ! [A] :
      ( ( v4_realset2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k2_realset2(A))
         => ! [C] :
              ( m1_subset_1(C,k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))))
             => ! [D] :
                  ( m1_subset_1(D,k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))))
                 => k1_funct_1(k2_realset3(A),k4_tarski(B,k1_funct_1(k2_realset3(A),k4_tarski(C,D)))) = k1_funct_1(k5_realset2(A),k4_tarski(k1_funct_1(k2_realset3(A),k4_tarski(B,C)),D)) ) ) ) ) )).

fof(t43_realset3,axiom,(
    ! [A] :
      ( ( v4_realset2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k2_realset2(A))
         => ! [C] :
              ( m1_subset_1(C,k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))))
             => ! [D] :
                  ( m1_subset_1(D,k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))))
                 => k1_funct_1(k2_realset3(A),k4_tarski(B,k1_funct_1(k5_realset2(A),k4_tarski(C,D)))) = k1_funct_1(k2_realset3(A),k4_tarski(k1_funct_1(k2_realset3(A),k4_tarski(B,C)),D)) ) ) ) ) )).

fof(dt_k1_realset3,axiom,(
    ! [A] :
      ( ( v4_realset2(A)
        & l3_vectsp_1(A) )
     => ( v1_funct_1(k1_realset3(A))
        & v1_funct_2(k1_realset3(A),k2_zfmisc_1(k2_realset2(A),k2_realset2(A)),k2_realset2(A))
        & m2_relset_1(k1_realset3(A),k2_zfmisc_1(k2_realset2(A),k2_realset2(A)),k2_realset2(A)) ) ) )).

fof(dt_k2_realset3,axiom,(
    ! [A] :
      ( ( v4_realset2(A)
        & l3_vectsp_1(A) )
     => ( v1_funct_1(k2_realset3(A))
        & v1_funct_2(k2_realset3(A),k2_zfmisc_1(k2_realset2(A),k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A)))),k2_realset2(A))
        & m2_relset_1(k2_realset3(A),k2_zfmisc_1(k2_realset2(A),k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A)))),k2_realset2(A)) ) ) )).
%------------------------------------------------------------------------------