SET007 Axioms: SET007+225.ax


%------------------------------------------------------------------------------
% File     : SET007+225 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Properties of Fields
% 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    : realset2 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   57 (   0 unit)
%            Number of atoms       :  368 (  71 equality)
%            Maximal formula depth :   36 (   8 average)
%            Number of connectives :  328 (  17 ~  ;   0  |; 154  &)
%                                         (  15 <=>; 142 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   21 (   0 propositional; 1-3 arity)
%            Number of functors    :   23 (   0 constant; 1-6 arity)
%            Number of variables   :  162 (   0 singleton; 140 !;  22 ?)
%            Maximal term depth    :    7 (   2 average)
% SPC      : 

% Comments : The individual reference can be found in [Mat90] by looking for
%            the name provided by [Urb08].
%          : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
%          : These set theory axioms are used in encodings of problems in
%            various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(rc1_realset2,axiom,(
    ? [A] :
      ( l1_rlvect_1(A)
      & ~ v3_struct_0(A)
      & v1_rlvect_1(A)
      & v3_rlvect_1(A)
      & v4_rlvect_1(A)
      & v1_realset2(A)
      & v2_realset2(A) ) )).

fof(rc2_realset2,axiom,(
    ? [A] :
      ( l1_struct_0(A)
      & v3_realset2(A) ) )).

fof(rc3_realset2,axiom,(
    ? [A] :
      ( l3_vectsp_1(A)
      & v3_vectsp_1(A)
      & ~ v3_realset2(A) ) )).

fof(rc4_realset2,axiom,(
    ? [A] :
      ( l3_vectsp_1(A)
      & v3_vectsp_1(A)
      & v4_realset2(A) ) )).

fof(d1_realset2,axiom,(
    ! [A] :
      ( l1_rlvect_1(A)
     => ( v1_realset2(A)
      <=> ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ( k1_binop_1(u1_rlvect_1(A),B,u2_struct_0(A)) = B
              & k1_binop_1(u1_rlvect_1(A),u2_struct_0(A),B) = B ) ) ) ) )).

fof(d2_realset2,axiom,(
    ! [A] :
      ( l1_rlvect_1(A)
     => ( v2_realset2(A)
      <=> ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ? [C] :
                ( m1_subset_1(C,u1_struct_0(A))
                & k1_binop_1(u1_rlvect_1(A),B,C) = u2_struct_0(A)
                & k1_binop_1(u1_rlvect_1(A),C,B) = u2_struct_0(A) ) ) ) ) )).

fof(d3_realset2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => ( v4_rlvect_1(A)
      <=> ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => k1_binop_1(u1_rlvect_1(A),k1_binop_1(u1_rlvect_1(A),B,C),D) = k1_binop_1(u1_rlvect_1(A),B,k1_binop_1(u1_rlvect_1(A),C,D)) ) ) ) ) ) )).

fof(d4_realset2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => ( v3_rlvect_1(A)
      <=> ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => k1_binop_1(u1_rlvect_1(A),B,C) = k1_binop_1(u1_rlvect_1(A),C,B) ) ) ) ) )).

fof(d5_realset2,axiom,(
    ! [A] :
      ( l1_struct_0(A)
     => ( v3_realset2(A)
      <=> v1_realset1(u1_struct_0(A)) ) ) )).

fof(d6_realset2,axiom,(
    ! [A] :
      ( ~ v1_realset1(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] :
              ( ( 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)
                 => ! [E] :
                      ( m1_subset_1(E,k4_xboole_0(A,k5_realset1(A,D)))
                     => ! [F] :
                          ( ( v3_vectsp_1(F)
                            & ~ v3_realset2(F)
                            & l3_vectsp_1(F) )
                         => ( F = k1_realset2(A,B,C,D,E)
                          <=> ( A = u1_struct_0(F)
                              & B = u1_rlvect_1(F)
                              & C = u1_group_1(F)
                              & D = u2_struct_0(F)
                              & E = u1_vectsp_1(F) ) ) ) ) ) ) ) ) )).

fof(d7_realset2,axiom,(
    ! [A] :
      ( l1_struct_0(A)
     => ( v3_realset2(A)
      <=> ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => B = C ) ) ) ) )).

fof(d8_realset2,axiom,(
    ! [A] :
      ( l3_vectsp_1(A)
     => ( v4_realset2(A)
      <=> ? [B] :
            ( ~ v1_realset1(B)
            & ? [C] :
                ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(B,B),B)
                & m2_relset_1(C,k2_zfmisc_1(B,B),B)
                & ? [D] :
                    ( m1_subset_1(D,B)
                    & ? [E] :
                        ( m3_realset1(E,B,D)
                        & ? [F] :
                            ( m1_subset_1(F,k4_xboole_0(B,k5_realset1(B,D)))
                            & A = k1_realset2(B,C,E,D,F)
                            & ~ v3_struct_0(g1_rlvect_1(B,C,D))
                            & v3_rlvect_1(g1_rlvect_1(B,C,D))
                            & v4_rlvect_1(g1_rlvect_1(B,C,D))
                            & v1_realset2(g1_rlvect_1(B,C,D))
                            & v2_realset2(g1_rlvect_1(B,C,D))
                            & l1_rlvect_1(g1_rlvect_1(B,C,D))
                            & ! [G] :
                                ( ~ v1_xboole_0(G)
                               => ! [H] :
                                    ( ( v1_funct_1(H)
                                      & v1_funct_2(H,k2_zfmisc_1(G,G),G)
                                      & m2_relset_1(H,k2_zfmisc_1(G,G),G) )
                                   => ! [I] :
                                        ( m1_subset_1(I,G)
                                       => ( ( G = k4_xboole_0(B,k5_realset1(B,D))
                                            & I = F
                                            & H = k4_realset1(B,D,E) )
                                         => ( ~ v3_struct_0(g1_rlvect_1(G,H,I))
                                            & v3_rlvect_1(g1_rlvect_1(G,H,I))
                                            & v4_rlvect_1(g1_rlvect_1(G,H,I))
                                            & v1_realset2(g1_rlvect_1(G,H,I))
                                            & v2_realset2(g1_rlvect_1(G,H,I))
                                            & l1_rlvect_1(g1_rlvect_1(G,H,I)) ) ) ) ) )
                            & ! [G] :
                                ( m1_subset_1(G,B)
                               => ! [H] :
                                    ( m1_subset_1(H,B)
                                   => ! [I] :
                                        ( m1_subset_1(I,B)
                                       => ( k1_funct_1(E,k4_tarski(G,k1_funct_1(C,k4_tarski(H,I)))) = k1_funct_1(C,k4_tarski(k1_funct_1(E,k4_tarski(G,H)),k1_funct_1(E,k4_tarski(G,I))))
                                          & k1_funct_1(E,k4_tarski(k1_funct_1(C,k4_tarski(G,H)),I)) = k1_funct_1(C,k4_tarski(k1_funct_1(E,k4_tarski(G,I)),k1_funct_1(E,k4_tarski(H,I)))) ) ) ) ) ) ) ) ) ) ) ) )).

fof(d9_realset2,axiom,(
    ! [A] :
      ( ( v4_realset2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ~ v1_realset1(B)
         => ( B = k2_realset2(A)
          <=> ? [C] :
                ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(B,B),B)
                & m2_relset_1(C,k2_zfmisc_1(B,B),B)
                & ? [D] :
                    ( m1_subset_1(D,B)
                    & ? [E] :
                        ( m3_realset1(E,B,D)
                        & ? [F] :
                            ( m1_subset_1(F,k4_xboole_0(B,k5_realset1(B,D)))
                            & A = k1_realset2(B,C,E,D,F) ) ) ) ) ) ) ) )).

fof(d10_realset2,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 = k3_realset2(A)
          <=> ? [C] :
                ( m1_subset_1(C,k2_realset2(A))
                & ? [D] :
                    ( m3_realset1(D,k2_realset2(A),C)
                    & ? [E] :
                        ( m1_subset_1(E,k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),C)))
                        & A = k1_realset2(k2_realset2(A),B,D,C,E) ) ) ) ) ) ) )).

fof(d11_realset2,axiom,(
    ! [A] :
      ( ( v4_realset2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k2_realset2(A))
         => ( B = k4_realset2(A)
          <=> ? [C] :
                ( m3_realset1(C,k2_realset2(A),B)
                & ? [D] :
                    ( m1_subset_1(D,k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),B)))
                    & A = k1_realset2(k2_realset2(A),k3_realset2(A),C,B,D) ) ) ) ) ) )).

fof(d12_realset2,axiom,(
    ! [A] :
      ( ( v4_realset2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m3_realset1(B,k2_realset2(A),k4_realset2(A))
         => ( B = k5_realset2(A)
          <=> ? [C] :
                ( m1_subset_1(C,k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))))
                & A = k1_realset2(k2_realset2(A),k3_realset2(A),B,k4_realset2(A),C) ) ) ) ) )).

fof(d13_realset2,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))))
         => ( B = k6_realset2(A)
          <=> A = k1_realset2(k2_realset2(A),k3_realset2(A),k5_realset2(A),k4_realset2(A),B) ) ) ) )).

fof(t1_realset2,axiom,(
    ! [A] :
      ( ( v4_realset2(A)
        & l3_vectsp_1(A) )
     => ( ~ v3_struct_0(g1_rlvect_1(k2_realset2(A),k3_realset2(A),k4_realset2(A)))
        & v3_rlvect_1(g1_rlvect_1(k2_realset2(A),k3_realset2(A),k4_realset2(A)))
        & v4_rlvect_1(g1_rlvect_1(k2_realset2(A),k3_realset2(A),k4_realset2(A)))
        & v1_realset2(g1_rlvect_1(k2_realset2(A),k3_realset2(A),k4_realset2(A)))
        & v2_realset2(g1_rlvect_1(k2_realset2(A),k3_realset2(A),k4_realset2(A)))
        & l1_rlvect_1(g1_rlvect_1(k2_realset2(A),k3_realset2(A),k4_realset2(A))) ) ) )).

fof(t2_realset2,axiom,(
    ! [A] :
      ( ( v4_realset2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(B,B),B)
                & m2_relset_1(C,k2_zfmisc_1(B,B),B) )
             => ! [D] :
                  ( m1_subset_1(D,B)
                 => ( ( B = k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A)))
                      & D = k6_realset2(A)
                      & C = k4_realset1(k2_realset2(A),k4_realset2(A),k5_realset2(A)) )
                   => ( ~ v3_struct_0(g1_rlvect_1(B,C,D))
                      & v3_rlvect_1(g1_rlvect_1(B,C,D))
                      & v4_rlvect_1(g1_rlvect_1(B,C,D))
                      & v1_realset2(g1_rlvect_1(B,C,D))
                      & v2_realset2(g1_rlvect_1(B,C,D))
                      & l1_rlvect_1(g1_rlvect_1(B,C,D)) ) ) ) ) ) ) )).

fof(t3_realset2,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(k3_realset2(A),k4_tarski(C,D)))) = k1_funct_1(k3_realset2(A),k4_tarski(k1_funct_1(k5_realset2(A),k4_tarski(B,C)),k1_funct_1(k5_realset2(A),k4_tarski(B,D))))
                    & k1_funct_1(k5_realset2(A),k4_tarski(k1_funct_1(k3_realset2(A),k4_tarski(B,C)),D)) = k1_funct_1(k3_realset2(A),k4_tarski(k1_funct_1(k5_realset2(A),k4_tarski(B,D)),k1_funct_1(k5_realset2(A),k4_tarski(C,D)))) ) ) ) ) ) )).

fof(t4_realset2,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))
                 => k2_binop_1(k2_realset2(A),k2_realset2(A),k2_realset2(A),k3_realset2(A),k2_binop_1(k2_realset2(A),k2_realset2(A),k2_realset2(A),k3_realset2(A),B,C),D) = k2_binop_1(k2_realset2(A),k2_realset2(A),k2_realset2(A),k3_realset2(A),B,k2_binop_1(k2_realset2(A),k2_realset2(A),k2_realset2(A),k3_realset2(A),C,D)) ) ) ) ) )).

fof(t5_realset2,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))
             => k2_binop_1(k2_realset2(A),k2_realset2(A),k2_realset2(A),k3_realset2(A),B,C) = k2_binop_1(k2_realset2(A),k2_realset2(A),k2_realset2(A),k3_realset2(A),C,B) ) ) ) )).

fof(t6_realset2,axiom,(
    ! [A] :
      ( ( v4_realset2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k2_realset2(A))
         => ( k2_binop_1(k2_realset2(A),k2_realset2(A),k2_realset2(A),k3_realset2(A),B,k4_realset2(A)) = B
            & k2_binop_1(k2_realset2(A),k2_realset2(A),k2_realset2(A),k3_realset2(A),k4_realset2(A),B) = B ) ) ) )).

fof(t7_realset2,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))
              & k2_binop_1(k2_realset2(A),k2_realset2(A),k2_realset2(A),k3_realset2(A),B,C) = k4_realset2(A)
              & k2_binop_1(k2_realset2(A),k2_realset2(A),k2_realset2(A),k3_realset2(A),C,B) = k4_realset2(A) ) ) ) )).

fof(t8_realset2,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))))
             => ! [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(k1_funct_1(k5_realset2(A),k4_tarski(B,C)),D)) = k1_funct_1(k5_realset2(A),k4_tarski(B,k1_funct_1(k5_realset2(A),k4_tarski(C,D)))) ) ) ) ) )).

fof(t9_realset2,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(k5_realset2(A),k4_tarski(B,C)) = k1_funct_1(k5_realset2(A),k4_tarski(C,B)) ) ) ) )).

fof(t10_realset2,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,k6_realset2(A))) = B
            & k1_funct_1(k5_realset2(A),k4_tarski(k6_realset2(A),B)) = B ) ) ) )).

fof(t11_realset2,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(k5_realset2(A),k4_tarski(B,C)) = k6_realset2(A)
              & k1_funct_1(k5_realset2(A),k4_tarski(C,B)) = k6_realset2(A) ) ) ) )).

fof(d14_realset2,axiom,(
    ! [A] :
      ( ( v4_realset2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k2_realset2(A),k2_realset2(A))
            & m2_relset_1(B,k2_realset2(A),k2_realset2(A)) )
         => ( B = k7_realset2(A)
          <=> ! [C] :
                ( m1_subset_1(C,k2_realset2(A))
               => k1_funct_1(k3_realset2(A),k4_tarski(C,k8_funct_2(k2_realset2(A),k2_realset2(A),B,C))) = k4_realset2(A) ) ) ) ) )).

fof(t12_realset2,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))
             => ( k2_binop_1(k2_realset2(A),k2_realset2(A),k2_realset2(A),k3_realset2(A),B,C) = k4_realset2(A)
               => C = k8_funct_2(k2_realset2(A),k2_realset2(A),k7_realset2(A),B) ) ) ) ) )).

fof(t13_realset2,axiom,(
    ! [A] :
      ( ( v4_realset2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k2_realset2(A))
         => B = k8_funct_2(k2_realset2(A),k2_realset2(A),k7_realset2(A),k8_funct_2(k2_realset2(A),k2_realset2(A),k7_realset2(A),B)) ) ) )).

fof(t14_realset2,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(k3_realset2(A),k4_tarski(B,C)),k2_realset2(A))
                & m1_subset_1(k1_funct_1(k5_realset2(A),k4_tarski(B,C)),k2_realset2(A))
                & m1_subset_1(k8_funct_2(k2_realset2(A),k2_realset2(A),k7_realset2(A),B),k2_realset2(A)) ) ) ) ) )).

fof(t15_realset2,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(k3_realset2(A),k4_tarski(C,k8_funct_2(k2_realset2(A),k2_realset2(A),k7_realset2(A),D))))) = k1_funct_1(k3_realset2(A),k4_tarski(k1_funct_1(k5_realset2(A),k4_tarski(B,C)),k1_funct_1(k7_realset2(A),k1_funct_1(k5_realset2(A),k4_tarski(B,D))))) ) ) ) ) )).

fof(t16_realset2,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(k3_realset2(A),k4_tarski(B,k8_funct_2(k2_realset2(A),k2_realset2(A),k7_realset2(A),C))),D)) = k1_funct_1(k3_realset2(A),k4_tarski(k1_funct_1(k5_realset2(A),k4_tarski(B,D)),k1_funct_1(k7_realset2(A),k1_funct_1(k5_realset2(A),k4_tarski(C,D))))) ) ) ) ) )).

fof(t17_realset2,axiom,(
    ! [A] :
      ( ( v4_realset2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k2_realset2(A))
         => k1_funct_1(k5_realset2(A),k4_tarski(B,k4_realset2(A))) = k4_realset2(A) ) ) )).

fof(t18_realset2,axiom,(
    ! [A] :
      ( ( v4_realset2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k2_realset2(A))
         => k1_funct_1(k5_realset2(A),k4_tarski(k4_realset2(A),B)) = k4_realset2(A) ) ) )).

fof(t19_realset2,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(k5_realset2(A),k4_tarski(B,C))) = k1_funct_1(k5_realset2(A),k4_tarski(B,k8_funct_2(k2_realset2(A),k2_realset2(A),k7_realset2(A),C))) ) ) ) )).

fof(t20_realset2,axiom,(
    ! [A] :
      ( ( v4_realset2(A)
        & l3_vectsp_1(A) )
     => k1_funct_1(k5_realset2(A),k4_tarski(k6_realset2(A),k4_realset2(A))) = k4_realset2(A) ) )).

fof(t21_realset2,axiom,(
    ! [A] :
      ( ( v4_realset2(A)
        & l3_vectsp_1(A) )
     => k1_funct_1(k5_realset2(A),k4_tarski(k4_realset2(A),k6_realset2(A))) = k4_realset2(A) ) )).

fof(t22_realset2,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(k5_realset2(A),k4_tarski(B,C)),k2_realset2(A)) ) ) ) )).

fof(t23_realset2,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(k5_realset2(A),k4_tarski(B,C)),D)) = k1_funct_1(k5_realset2(A),k4_tarski(B,k1_funct_1(k5_realset2(A),k4_tarski(C,D)))) ) ) ) ) )).

fof(t24_realset2,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)) = k1_funct_1(k5_realset2(A),k4_tarski(C,B)) ) ) ) )).

fof(t25_realset2,axiom,(
    ! [A] :
      ( ( v4_realset2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k2_realset2(A))
         => ( k1_funct_1(k5_realset2(A),k4_tarski(B,k6_realset2(A))) = B
            & k1_funct_1(k5_realset2(A),k4_tarski(k6_realset2(A),B)) = B ) ) ) )).

fof(d15_realset2,axiom,(
    ! [A] :
      ( ( v4_realset2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,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))))
            & m2_relset_1(B,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)))) )
         => ( B = k8_realset2(A)
          <=> ! [C] :
                ( m1_subset_1(C,k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))))
               => 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))),B,C))) = k6_realset2(A) ) ) ) ) )).

fof(t26_realset2,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(k5_realset2(A),k4_tarski(B,C)) = k6_realset2(A)
               => 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(t27_realset2,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))))
         => 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),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(t28_realset2,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))))
             => ( m1_subset_1(k1_funct_1(k5_realset2(A),k4_tarski(B,C)),k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))))
                & m1_subset_1(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),k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A)))) ) ) ) ) )).

fof(t29_realset2,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))
                 => ( k2_binop_1(k2_realset2(A),k2_realset2(A),k2_realset2(A),k3_realset2(A),B,C) = k2_binop_1(k2_realset2(A),k2_realset2(A),k2_realset2(A),k3_realset2(A),B,D)
                   => C = D ) ) ) ) ) )).

fof(t30_realset2,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)) = k1_funct_1(k5_realset2(A),k4_tarski(B,D))
                   => C = D ) ) ) ) ) )).

fof(dt_k1_realset2,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v1_realset1(A)
        & v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(A,A),A)
        & m1_relset_1(B,k2_zfmisc_1(A,A),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(D,A)
        & m1_subset_1(E,k4_xboole_0(A,k5_realset1(A,D))) )
     => ( v3_vectsp_1(k1_realset2(A,B,C,D,E))
        & ~ v3_realset2(k1_realset2(A,B,C,D,E))
        & l3_vectsp_1(k1_realset2(A,B,C,D,E)) ) ) )).

fof(dt_k2_realset2,axiom,(
    ! [A] :
      ( ( v4_realset2(A)
        & l3_vectsp_1(A) )
     => ~ v1_realset1(k2_realset2(A)) ) )).

fof(dt_k3_realset2,axiom,(
    ! [A] :
      ( ( v4_realset2(A)
        & l3_vectsp_1(A) )
     => ( v1_funct_1(k3_realset2(A))
        & v1_funct_2(k3_realset2(A),k2_zfmisc_1(k2_realset2(A),k2_realset2(A)),k2_realset2(A))
        & m2_relset_1(k3_realset2(A),k2_zfmisc_1(k2_realset2(A),k2_realset2(A)),k2_realset2(A)) ) ) )).

fof(dt_k4_realset2,axiom,(
    ! [A] :
      ( ( v4_realset2(A)
        & l3_vectsp_1(A) )
     => m1_subset_1(k4_realset2(A),k2_realset2(A)) ) )).

fof(dt_k5_realset2,axiom,(
    ! [A] :
      ( ( v4_realset2(A)
        & l3_vectsp_1(A) )
     => m3_realset1(k5_realset2(A),k2_realset2(A),k4_realset2(A)) ) )).

fof(dt_k6_realset2,axiom,(
    ! [A] :
      ( ( v4_realset2(A)
        & l3_vectsp_1(A) )
     => m1_subset_1(k6_realset2(A),k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A)))) ) )).

fof(dt_k7_realset2,axiom,(
    ! [A] :
      ( ( v4_realset2(A)
        & l3_vectsp_1(A) )
     => ( v1_funct_1(k7_realset2(A))
        & v1_funct_2(k7_realset2(A),k2_realset2(A),k2_realset2(A))
        & m2_relset_1(k7_realset2(A),k2_realset2(A),k2_realset2(A)) ) ) )).

fof(dt_k8_realset2,axiom,(
    ! [A] :
      ( ( v4_realset2(A)
        & l3_vectsp_1(A) )
     => ( v1_funct_1(k8_realset2(A))
        & v1_funct_2(k8_realset2(A),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))))
        & m2_relset_1(k8_realset2(A),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)))) ) ) )).
%------------------------------------------------------------------------------