SET007 Axioms: SET007+302.ax


%------------------------------------------------------------------------------
% File     : SET007+302 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Atlas of Midpoint Algebra
% 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    : midsp_2 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   80 (   6 unit)
%            Number of atoms       :  818 ( 104 equality)
%            Maximal formula depth :   27 (  10 average)
%            Number of connectives :  852 ( 114 ~  ;   0  |; 432  &)
%                                         (  19 <=>; 287 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   26 (   1 propositional; 0-3 arity)
%            Number of functors    :   28 (   0 constant; 1-6 arity)
%            Number of variables   :  292 (   0 singleton; 281 !;  11 ?)
%            Maximal term depth    :    5 (   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(fc1_midsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_midsp_1(A)
        & l1_midsp_1(A) )
     => ( ~ v3_struct_0(k19_midsp_1(A))
        & v1_rlvect_1(k19_midsp_1(A))
        & v3_rlvect_1(k19_midsp_1(A))
        & v4_rlvect_1(k19_midsp_1(A))
        & v5_rlvect_1(k19_midsp_1(A))
        & v6_rlvect_1(k19_midsp_1(A)) ) ) )).

fof(cc1_midsp_2,axiom,(
    ! [A] :
      ( l1_rlvect_1(A)
     => ( ( ~ v3_struct_0(A)
          & v1_midsp_2(A) )
       => ( ~ v3_struct_0(A)
          & v13_vectsp_1(A) ) ) ) )).

fof(rc1_midsp_2,axiom,(
    ? [A] :
      ( l1_rlvect_1(A)
      & ~ v3_struct_0(A)
      & v1_rlvect_1(A)
      & v3_rlvect_1(A)
      & v4_rlvect_1(A)
      & v5_rlvect_1(A)
      & v6_rlvect_1(A)
      & v13_vectsp_1(A)
      & v1_midsp_2(A) ) )).

fof(fc2_midsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_midsp_1(A)
        & l1_midsp_1(A) )
     => ( ~ v3_struct_0(k19_midsp_1(A))
        & v1_rlvect_1(k19_midsp_1(A))
        & v3_rlvect_1(k19_midsp_1(A))
        & v4_rlvect_1(k19_midsp_1(A))
        & v5_rlvect_1(k19_midsp_1(A))
        & v6_rlvect_1(k19_midsp_1(A))
        & v13_vectsp_1(k19_midsp_1(A))
        & v1_midsp_2(k19_midsp_1(A)) ) ) )).

fof(fc3_midsp_2,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(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) )
     => ( ~ v3_struct_0(g1_midsp_1(A,B))
        & v1_midsp_1(g1_midsp_1(A,B)) ) ) )).

fof(rc2_midsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_midsp_1(A) )
     => ? [B] :
          ( l1_midsp_2(B,A)
          & v2_midsp_2(B,A) ) ) )).

fof(rc3_midsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_midsp_1(A)
        & l1_midsp_1(A) )
     => ? [B] :
          ( l1_midsp_2(B,A)
          & v3_midsp_2(B,A) ) ) )).

fof(d1_midsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k1_midsp_2(A,B) = k2_rlvect_1(A,B,B) ) ) )).

fof(d2_midsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_midsp_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_rlvect_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(B))
                & m2_relset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(B)) )
             => ( r1_midsp_2(A,B,C)
              <=> ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ! [F] :
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ( k1_midsp_1(A,D,E) = F
                            <=> k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(B),C,D,F) = k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(B),C,F,E) ) ) ) ) ) ) ) ) )).

fof(t1_midsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_midsp_1(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A))
                    & m2_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A)) )
                 => ( r1_midsp_2(B,A,D)
                   => k1_midsp_1(B,C,C) = C ) ) ) ) ) )).

fof(d3_midsp_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_rlvect_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
                & m2_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
             => ( r2_midsp_2(A,B,C)
              <=> ( ! [D] :
                      ( m1_subset_1(D,A)
                     => ! [E] :
                          ( m1_subset_1(E,u1_struct_0(B))
                         => ? [F] :
                              ( m1_subset_1(F,A)
                              & k2_binop_1(A,A,u1_struct_0(B),C,D,F) = E ) ) )
                  & ! [D] :
                      ( m1_subset_1(D,A)
                     => ! [E] :
                          ( m1_subset_1(E,A)
                         => ! [F] :
                              ( m1_subset_1(F,A)
                             => ( k2_binop_1(A,A,u1_struct_0(B),C,D,E) = k2_binop_1(A,A,u1_struct_0(B),C,D,F)
                               => E = F ) ) ) )
                  & ! [D] :
                      ( m1_subset_1(D,A)
                     => ! [E] :
                          ( m1_subset_1(E,A)
                         => ! [F] :
                              ( m1_subset_1(F,A)
                             => k2_rlvect_1(B,k2_binop_1(A,A,u1_struct_0(B),C,D,E),k2_binop_1(A,A,u1_struct_0(B),C,E,F)) = k2_binop_1(A,A,u1_struct_0(B),C,D,F) ) ) ) ) ) ) ) ) )).

fof(d4_midsp_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_rlvect_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
                & m2_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
             => ! [D] :
                  ( m1_subset_1(D,A)
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(B))
                     => ( r2_midsp_2(A,B,C)
                       => ! [F] :
                            ( m1_subset_1(F,A)
                           => ( F = k2_midsp_2(A,B,C,D,E)
                            <=> k2_binop_1(A,A,u1_struct_0(B),C,D,F) = E ) ) ) ) ) ) ) ) )).

fof(t2_midsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => k1_midsp_2(A,k1_rlvect_1(A)) = k1_rlvect_1(A) ) )).

fof(t3_midsp_2,axiom,(
    $true )).

fof(t4_midsp_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,A)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & l1_rlvect_1(C) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k2_zfmisc_1(A,A),u1_struct_0(C))
                    & m2_relset_1(D,k2_zfmisc_1(A,A),u1_struct_0(C)) )
                 => ( r2_midsp_2(A,C,D)
                   => k2_binop_1(A,A,u1_struct_0(C),D,B,B) = k1_rlvect_1(C) ) ) ) ) ) )).

fof(t5_midsp_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,A)
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & v4_rlvect_1(D)
                    & v5_rlvect_1(D)
                    & v6_rlvect_1(D)
                    & l1_rlvect_1(D) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k2_zfmisc_1(A,A),u1_struct_0(D))
                        & m2_relset_1(E,k2_zfmisc_1(A,A),u1_struct_0(D)) )
                     => ( ( r2_midsp_2(A,D,E)
                          & k2_binop_1(A,A,u1_struct_0(D),E,B,C) = k1_rlvect_1(D) )
                       => B = C ) ) ) ) ) ) )).

fof(t6_midsp_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,A)
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & v4_rlvect_1(D)
                    & v5_rlvect_1(D)
                    & v6_rlvect_1(D)
                    & l1_rlvect_1(D) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k2_zfmisc_1(A,A),u1_struct_0(D))
                        & m2_relset_1(E,k2_zfmisc_1(A,A),u1_struct_0(D)) )
                     => ( r2_midsp_2(A,D,E)
                       => k2_binop_1(A,A,u1_struct_0(D),E,B,C) = k5_rlvect_1(D,k2_binop_1(A,A,u1_struct_0(D),E,C,B)) ) ) ) ) ) ) )).

fof(t7_midsp_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,A)
             => ! [D] :
                  ( m1_subset_1(D,A)
                 => ! [E] :
                      ( m1_subset_1(E,A)
                     => ! [F] :
                          ( ( ~ v3_struct_0(F)
                            & v4_rlvect_1(F)
                            & v5_rlvect_1(F)
                            & v6_rlvect_1(F)
                            & l1_rlvect_1(F) )
                         => ! [G] :
                              ( ( v1_funct_1(G)
                                & v1_funct_2(G,k2_zfmisc_1(A,A),u1_struct_0(F))
                                & m2_relset_1(G,k2_zfmisc_1(A,A),u1_struct_0(F)) )
                             => ( ( r2_midsp_2(A,F,G)
                                  & k2_binop_1(A,A,u1_struct_0(F),G,B,C) = k2_binop_1(A,A,u1_struct_0(F),G,D,E) )
                               => k2_binop_1(A,A,u1_struct_0(F),G,C,B) = k2_binop_1(A,A,u1_struct_0(F),G,E,D) ) ) ) ) ) ) ) ) )).

fof(t8_midsp_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & l1_rlvect_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
                & m2_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
             => ( r2_midsp_2(A,B,C)
               => ! [D] :
                    ( m1_subset_1(D,A)
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(B))
                       => ? [F] :
                            ( m1_subset_1(F,A)
                            & k2_binop_1(A,A,u1_struct_0(B),C,F,D) = E ) ) ) ) ) ) ) )).

fof(t9_midsp_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,A)
             => ! [D] :
                  ( m1_subset_1(D,A)
                 => ! [E] :
                      ( ( ~ v3_struct_0(E)
                        & v4_rlvect_1(E)
                        & v5_rlvect_1(E)
                        & v6_rlvect_1(E)
                        & l1_rlvect_1(E) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,k2_zfmisc_1(A,A),u1_struct_0(E))
                            & m2_relset_1(F,k2_zfmisc_1(A,A),u1_struct_0(E)) )
                         => ( ( r2_midsp_2(A,E,F)
                              & k2_binop_1(A,A,u1_struct_0(E),F,B,C) = k2_binop_1(A,A,u1_struct_0(E),F,D,C) )
                           => B = D ) ) ) ) ) ) ) )).

fof(t10_midsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_midsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & v4_rlvect_1(D)
                    & v5_rlvect_1(D)
                    & v6_rlvect_1(D)
                    & l1_rlvect_1(D) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(D))
                        & m2_relset_1(E,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(D)) )
                     => ( ( r2_midsp_2(u1_struct_0(A),D,E)
                          & r1_midsp_2(A,D,E) )
                       => k1_midsp_1(A,B,C) = k1_midsp_1(A,C,B) ) ) ) ) ) ) )).

fof(t11_midsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_midsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & v4_rlvect_1(D)
                    & v5_rlvect_1(D)
                    & v6_rlvect_1(D)
                    & l1_rlvect_1(D) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(D))
                        & m2_relset_1(E,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(D)) )
                     => ~ ( r2_midsp_2(u1_struct_0(A),D,E)
                          & r1_midsp_2(A,D,E)
                          & ! [F] :
                              ( m1_subset_1(F,u1_struct_0(A))
                             => k1_midsp_1(A,F,B) != C ) ) ) ) ) ) ) )).

fof(t12_midsp_2,axiom,(
    $true )).

fof(t13_midsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & l1_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))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => k4_rlvect_1(A,k4_rlvect_1(A,B,C),k4_rlvect_1(A,D,E)) = k4_rlvect_1(A,k4_rlvect_1(A,B,D),k4_rlvect_1(A,C,E)) ) ) ) ) ) )).

fof(t14_midsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k1_midsp_2(A,k4_rlvect_1(A,B,C)) = k4_rlvect_1(A,k1_midsp_2(A,B),k1_midsp_2(A,C)) ) ) ) )).

fof(t15_midsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k1_midsp_2(A,k5_rlvect_1(A,B)) = k5_rlvect_1(A,k1_midsp_2(A,B)) ) ) )).

fof(t16_midsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_midsp_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & l1_rlvect_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(B))
                & m2_relset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(B)) )
             => ( ( r2_midsp_2(u1_struct_0(A),B,C)
                  & r1_midsp_2(A,B,C) )
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ! [F] :
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ! [G] :
                                ( m1_subset_1(G,u1_struct_0(A))
                               => ( k1_midsp_1(A,D,E) = k1_midsp_1(A,F,G)
                                <=> k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(B),C,D,G) = k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(B),C,F,E) ) ) ) ) ) ) ) ) ) )).

fof(t17_midsp_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & l1_rlvect_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
                & m2_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
             => ( r2_midsp_2(A,B,C)
               => ! [D] :
                    ( m1_subset_1(D,A)
                   => ! [E] :
                        ( m1_subset_1(E,A)
                       => ! [F] :
                            ( m1_subset_1(F,A)
                           => ! [G] :
                                ( m1_subset_1(G,A)
                               => ! [H] :
                                    ( m1_subset_1(H,A)
                                   => ( ( k2_binop_1(A,A,u1_struct_0(B),C,D,E) = k2_binop_1(A,A,u1_struct_0(B),C,E,G)
                                        & k2_binop_1(A,A,u1_struct_0(B),C,D,F) = k2_binop_1(A,A,u1_struct_0(B),C,F,H) )
                                     => k2_binop_1(A,A,u1_struct_0(B),C,G,H) = k1_midsp_2(B,k2_binop_1(A,A,u1_struct_0(B),C,E,F)) ) ) ) ) ) ) ) ) ) ) )).

fof(t18_midsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_midsp_1(A)
        & l1_midsp_1(A) )
     => ( ! [B] :
            ( m1_subset_1(B,u1_struct_0(k19_midsp_1(A)))
          <=> m1_midsp_1(B,A) )
        & k1_rlvect_1(k19_midsp_1(A)) = k10_midsp_1(A)
        & ! [B] :
            ( m1_subset_1(B,u1_struct_0(k19_midsp_1(A)))
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(k19_midsp_1(A)))
               => ! [D] :
                    ( m1_midsp_1(D,A)
                   => ! [E] :
                        ( m1_midsp_1(E,A)
                       => ( ( B = D
                            & C = E )
                         => k4_rlvect_1(k19_midsp_1(A),B,C) = k11_midsp_1(A,D,E) ) ) ) ) ) ) ) )).

fof(d5_midsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => ( v1_midsp_2(A)
      <=> ( ! [B] :
              ( m1_subset_1(B,u1_struct_0(A))
             => ? [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                  & k1_midsp_2(A,C) = B ) )
          & ! [B] :
              ( m1_subset_1(B,u1_struct_0(A))
             => ( k1_midsp_2(A,B) = k1_rlvect_1(A)
               => B = k1_rlvect_1(A) ) ) ) ) ) )).

fof(t19_midsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v13_vectsp_1(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( B = k5_rlvect_1(A,B)
           => B = k1_rlvect_1(A) ) ) ) )).

fof(t20_midsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v13_vectsp_1(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( k1_midsp_2(A,B) = k1_midsp_2(A,C)
               => B = C ) ) ) ) )).

fof(d6_midsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v1_midsp_2(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( C = k3_midsp_2(A,B)
              <=> k1_midsp_2(A,C) = B ) ) ) ) )).

fof(t21_midsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v1_midsp_2(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( k3_midsp_2(A,k1_rlvect_1(A)) = k1_rlvect_1(A)
                & k3_midsp_2(A,k4_rlvect_1(A,B,C)) = k4_rlvect_1(A,k3_midsp_2(A,B),k3_midsp_2(A,C))
                & ( k3_midsp_2(A,B) = k3_midsp_2(A,C)
                 => B = C )
                & k3_midsp_2(A,k1_midsp_2(A,B)) = B ) ) ) ) )).

fof(t22_midsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v1_midsp_2(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_midsp_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A))
                & m2_relset_1(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A)) )
             => ( ( r2_midsp_2(u1_struct_0(B),A,C)
                  & r1_midsp_2(B,A,C) )
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(B))
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(B))
                       => ! [F] :
                            ( m1_subset_1(F,u1_struct_0(B))
                           => ! [G] :
                                ( m1_subset_1(G,u1_struct_0(B))
                               => k1_midsp_1(B,k1_midsp_1(B,D,E),k1_midsp_1(B,F,G)) = k1_midsp_1(B,k1_midsp_1(B,D,F),k1_midsp_1(B,E,G)) ) ) ) ) ) ) ) ) )).

fof(t23_midsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v1_midsp_2(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_midsp_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A))
                & m2_relset_1(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A)) )
             => ( ( r2_midsp_2(u1_struct_0(B),A,C)
                  & r1_midsp_2(B,A,C) )
               => ( ~ v3_struct_0(B)
                  & v2_midsp_1(B)
                  & l1_midsp_1(B) ) ) ) ) ) )).

fof(d7_midsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_midsp_1(A)
        & l1_midsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k4_midsp_2(A,B,C) = k12_midsp_1(A,B,C) ) ) ) )).

fof(d8_midsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_midsp_1(A)
        & l1_midsp_1(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k19_midsp_1(A)))
            & m2_relset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k19_midsp_1(A))) )
         => ( B = k5_midsp_2(A)
          <=> ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(k19_midsp_1(A)),B,C,D) = k12_midsp_1(A,C,D) ) ) ) ) ) )).

fof(t24_midsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_midsp_1(A)
        & l1_midsp_1(A) )
     => r2_midsp_2(u1_struct_0(A),k19_midsp_1(A),k5_midsp_2(A)) ) )).

fof(t25_midsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_midsp_1(A)
        & l1_midsp_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))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( k12_midsp_1(A,B,C) = k12_midsp_1(A,D,E)
                      <=> k4_midsp_1(A,B,E) = k4_midsp_1(A,C,D) ) ) ) ) ) ) )).

fof(t26_midsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_midsp_1(A)
        & l1_midsp_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))
                 => ( k4_midsp_1(A,B,C) = D
                  <=> k12_midsp_1(A,B,D) = k12_midsp_1(A,D,C) ) ) ) ) ) )).

fof(t27_midsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_midsp_1(A)
        & l1_midsp_1(A) )
     => r1_midsp_2(A,k19_midsp_1(A),k5_midsp_2(A)) ) )).

fof(d9_midsp_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v1_midsp_2(B)
            & l1_rlvect_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
                & m2_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
             => ( r2_midsp_2(A,B,C)
               => ! [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) )
                   => ( D = k6_midsp_2(A,B,C)
                    <=> ! [E] :
                          ( m1_subset_1(E,A)
                         => ! [F] :
                              ( m1_subset_1(F,A)
                             => k2_binop_1(A,A,u1_struct_0(B),C,E,k2_binop_1(A,A,A,D,E,F)) = k2_binop_1(A,A,u1_struct_0(B),C,k2_binop_1(A,A,A,D,E,F),F) ) ) ) ) ) ) ) ) )).

fof(t28_midsp_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v1_midsp_2(B)
            & l1_rlvect_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
                & m2_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
             => ( r2_midsp_2(A,B,C)
               => ! [D] :
                    ( m1_subset_1(D,A)
                   => ! [E] :
                        ( m1_subset_1(E,A)
                       => ! [F] :
                            ( m1_subset_1(F,A)
                           => ( k2_binop_1(A,A,A,k6_midsp_2(A,B,C),D,E) = F
                            <=> k2_binop_1(A,A,u1_struct_0(B),C,D,F) = k2_binop_1(A,A,u1_struct_0(B),C,F,E) ) ) ) ) ) ) ) ) )).

fof(d10_midsp_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v1_midsp_2(B)
            & l1_rlvect_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
                & m2_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
             => k7_midsp_2(A,B,C) = C ) ) ) )).

fof(t29_midsp_2,axiom,(
    $true )).

fof(t30_midsp_2,axiom,(
    $true )).

fof(t31_midsp_2,axiom,(
    $true )).

fof(t32_midsp_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v1_midsp_2(B)
            & l1_rlvect_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
                & m2_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
             => ( r2_midsp_2(A,B,C)
               => r1_midsp_2(g1_midsp_1(A,k6_midsp_2(A,B,C)),B,k7_midsp_2(A,B,C)) ) ) ) ) )).

fof(d11_midsp_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v1_midsp_2(B)
            & l1_rlvect_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
                & m2_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
             => ( r2_midsp_2(A,B,C)
               => k8_midsp_2(A,B,C) = g1_midsp_1(A,k6_midsp_2(A,B,C)) ) ) ) ) )).

fof(t33_midsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_midsp_1(A) )
     => ( ( ~ v3_struct_0(A)
          & v2_midsp_1(A)
          & l1_midsp_1(A) )
      <=> ? [B] :
            ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v1_midsp_2(B)
            & l1_rlvect_1(B)
            & ? [C] :
                ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(B))
                & m2_relset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(B))
                & r2_midsp_2(u1_struct_0(A),B,C)
                & r1_midsp_2(A,B,C) ) ) ) ) )).

fof(d12_midsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_midsp_1(A) )
     => ! [B] :
          ( l1_midsp_2(B,A)
         => ( v3_midsp_2(B,A)
          <=> ( v1_midsp_2(u1_midsp_2(A,B))
              & v4_rlvect_1(u1_midsp_2(A,B))
              & v5_rlvect_1(u1_midsp_2(A,B))
              & v6_rlvect_1(u1_midsp_2(A,B))
              & v3_rlvect_1(u1_midsp_2(A,B))
              & r1_midsp_2(A,u1_midsp_2(A,B),u2_midsp_2(A,B))
              & r2_midsp_2(u1_struct_0(A),u1_midsp_2(A,B),u2_midsp_2(A,B)) ) ) ) ) )).

fof(d13_midsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_midsp_1(A)
        & l1_midsp_1(A) )
     => ! [B] :
          ( l1_midsp_2(B,A)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => k9_midsp_2(A,B,C,D) = k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(u1_midsp_2(A,B)),u2_midsp_2(A,B),C,D) ) ) ) ) )).

fof(d14_midsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_midsp_1(A)
        & l1_midsp_1(A) )
     => ! [B] :
          ( l1_midsp_2(B,A)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(u1_midsp_2(A,B)))
                 => k10_midsp_2(A,B,C,D) = k2_midsp_2(u1_struct_0(A),u1_midsp_2(A,B),u2_midsp_2(A,B),C,D) ) ) ) ) )).

fof(d15_midsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_midsp_1(A)
        & l1_midsp_1(A) )
     => ! [B] :
          ( ( v3_midsp_2(B,A)
            & l1_midsp_2(B,A) )
         => k11_midsp_2(A,B) = k1_rlvect_1(u1_midsp_2(A,B)) ) ) )).

fof(t34_midsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v1_midsp_2(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_midsp_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A))
                & m2_relset_1(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A)) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(B))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(B))
                         => ! [G] :
                              ( m1_subset_1(G,u1_struct_0(B))
                             => ( ( r2_midsp_2(u1_struct_0(B),A,C)
                                  & r1_midsp_2(B,A,C) )
                               => ( k1_midsp_1(B,D,E) = k1_midsp_1(B,F,G)
                                <=> k2_binop_1(u1_struct_0(B),u1_struct_0(B),u1_struct_0(A),C,D,E) = k4_rlvect_1(A,k2_binop_1(u1_struct_0(B),u1_struct_0(B),u1_struct_0(A),C,D,F),k2_binop_1(u1_struct_0(B),u1_struct_0(B),u1_struct_0(A),C,D,G)) ) ) ) ) ) ) ) ) ) )).

fof(t35_midsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v1_midsp_2(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_midsp_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A))
                & m2_relset_1(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A)) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(B))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(B))
                         => ( ( r2_midsp_2(u1_struct_0(B),A,C)
                              & r1_midsp_2(B,A,C) )
                           => ( k1_midsp_1(B,D,E) = F
                            <=> k2_binop_1(u1_struct_0(B),u1_struct_0(B),u1_struct_0(A),C,D,E) = k1_midsp_2(A,k2_binop_1(u1_struct_0(B),u1_struct_0(B),u1_struct_0(A),C,D,F)) ) ) ) ) ) ) ) ) )).

fof(t36_midsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_midsp_1(A)
        & l1_midsp_1(A) )
     => ! [B] :
          ( ( v3_midsp_2(B,A)
            & l1_midsp_2(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ( k4_midsp_1(A,C,D) = k4_midsp_1(A,E,F)
                          <=> k9_midsp_2(A,B,C,D) = k2_rlvect_1(u1_midsp_2(A,B),k9_midsp_2(A,B,C,E),k9_midsp_2(A,B,C,F)) ) ) ) ) ) ) ) )).

fof(t37_midsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_midsp_1(A)
        & l1_midsp_1(A) )
     => ! [B] :
          ( ( v3_midsp_2(B,A)
            & l1_midsp_2(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( k4_midsp_1(A,C,D) = E
                      <=> k9_midsp_2(A,B,C,D) = k1_midsp_2(u1_midsp_2(A,B),k9_midsp_2(A,B,C,E)) ) ) ) ) ) ) )).

fof(t38_midsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_midsp_1(A)
        & l1_midsp_1(A) )
     => ! [B] :
          ( ( v3_midsp_2(B,A)
            & l1_midsp_2(B,A) )
         => ( ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(u1_midsp_2(A,B)))
                   => ? [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                        & k9_midsp_2(A,B,C,E) = D ) ) )
            & ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ( k9_midsp_2(A,B,C,D) = k9_midsp_2(A,B,C,E)
                         => D = E ) ) ) )
            & ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => k2_rlvect_1(u1_midsp_2(A,B),k9_midsp_2(A,B,C,D),k9_midsp_2(A,B,D,E)) = k9_midsp_2(A,B,C,E) ) ) ) ) ) ) )).

fof(t39_midsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_midsp_1(A)
        & l1_midsp_1(A) )
     => ! [B] :
          ( ( v3_midsp_2(B,A)
            & l1_midsp_2(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ! [G] :
                              ( m1_subset_1(G,u1_struct_0(u1_midsp_2(A,B)))
                             => ( k9_midsp_2(A,B,C,C) = k11_midsp_2(A,B)
                                & ( k9_midsp_2(A,B,C,D) = k11_midsp_2(A,B)
                                 => C = D )
                                & k9_midsp_2(A,B,C,D) = k5_rlvect_1(u1_midsp_2(A,B),k9_midsp_2(A,B,D,C))
                                & ( k9_midsp_2(A,B,C,D) = k9_midsp_2(A,B,E,F)
                                 => k9_midsp_2(A,B,D,C) = k9_midsp_2(A,B,F,E) )
                                & ! [H] :
                                    ( m1_subset_1(H,u1_struct_0(A))
                                   => ! [I] :
                                        ( m1_subset_1(I,u1_struct_0(u1_midsp_2(A,B)))
                                       => ? [J] :
                                            ( m1_subset_1(J,u1_struct_0(A))
                                            & k9_midsp_2(A,B,J,H) = I ) ) )
                                & ( k9_midsp_2(A,B,D,C) = k9_midsp_2(A,B,E,C)
                                 => D = E )
                                & ( k4_midsp_1(A,C,D) = E
                                 => k9_midsp_2(A,B,C,E) = k9_midsp_2(A,B,E,D) )
                                & ( k9_midsp_2(A,B,C,E) = k9_midsp_2(A,B,E,D)
                                 => k4_midsp_1(A,C,D) = E )
                                & ( k4_midsp_1(A,C,D) = k4_midsp_1(A,E,F)
                                 => k9_midsp_2(A,B,C,F) = k9_midsp_2(A,B,E,D) )
                                & ( k9_midsp_2(A,B,C,F) = k9_midsp_2(A,B,E,D)
                                 => k4_midsp_1(A,C,D) = k4_midsp_1(A,E,F) )
                                & ( k9_midsp_2(A,B,C,D) = G
                                 => k10_midsp_2(A,B,C,G) = D )
                                & ( k10_midsp_2(A,B,C,G) = D
                                 => k9_midsp_2(A,B,C,D) = G ) ) ) ) ) ) ) ) ) )).

fof(t40_midsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_midsp_1(A)
        & l1_midsp_1(A) )
     => ! [B] :
          ( ( v3_midsp_2(B,A)
            & l1_midsp_2(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k10_midsp_2(A,B,C,k11_midsp_2(A,B)) = C ) ) ) )).

fof(dt_l1_midsp_2,axiom,(
    $true )).

fof(existence_l1_midsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_midsp_1(A) )
     => ? [B] : l1_midsp_2(B,A) ) )).

fof(abstractness_v2_midsp_2,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_midsp_1(A)
        & l1_midsp_2(B,A) )
     => ( v2_midsp_2(B,A)
       => B = g1_midsp_2(A,u1_midsp_2(A,B),u2_midsp_2(A,B)) ) ) )).

fof(dt_k1_midsp_2,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => m1_subset_1(k1_midsp_2(A,B),u1_struct_0(A)) ) )).

fof(dt_k2_midsp_2,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v1_xboole_0(A)
        & ~ v3_struct_0(B)
        & l1_rlvect_1(B)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
        & m1_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B))
        & m1_subset_1(D,A)
        & m1_subset_1(E,u1_struct_0(B)) )
     => m1_subset_1(k2_midsp_2(A,B,C,D,E),A) ) )).

fof(dt_k3_midsp_2,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v1_midsp_2(A)
        & l1_rlvect_1(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => m1_subset_1(k3_midsp_2(A,B),u1_struct_0(A)) ) )).

fof(dt_k4_midsp_2,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v2_midsp_1(A)
        & l1_midsp_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k4_midsp_2(A,B,C),u1_struct_0(k19_midsp_1(A))) ) )).

fof(dt_k5_midsp_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_midsp_1(A)
        & l1_midsp_1(A) )
     => ( v1_funct_1(k5_midsp_2(A))
        & v1_funct_2(k5_midsp_2(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k19_midsp_1(A)))
        & m2_relset_1(k5_midsp_2(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k19_midsp_1(A))) ) ) )).

fof(dt_k6_midsp_2,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v1_midsp_2(B)
        & l1_rlvect_1(B)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
        & m1_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
     => ( v1_funct_1(k6_midsp_2(A,B,C))
        & v1_funct_2(k6_midsp_2(A,B,C),k2_zfmisc_1(A,A),A)
        & m2_relset_1(k6_midsp_2(A,B,C),k2_zfmisc_1(A,A),A) ) ) )).

fof(dt_k7_midsp_2,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v1_midsp_2(B)
        & l1_rlvect_1(B)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
        & m1_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
     => ( v1_funct_1(k7_midsp_2(A,B,C))
        & v1_funct_2(k7_midsp_2(A,B,C),k2_zfmisc_1(u1_struct_0(g1_midsp_1(A,k6_midsp_2(A,B,C))),u1_struct_0(g1_midsp_1(A,k6_midsp_2(A,B,C)))),u1_struct_0(B))
        & m2_relset_1(k7_midsp_2(A,B,C),k2_zfmisc_1(u1_struct_0(g1_midsp_1(A,k6_midsp_2(A,B,C))),u1_struct_0(g1_midsp_1(A,k6_midsp_2(A,B,C)))),u1_struct_0(B)) ) ) )).

fof(dt_k8_midsp_2,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v1_midsp_2(B)
        & l1_rlvect_1(B)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
        & m1_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
     => ( ~ v3_struct_0(k8_midsp_2(A,B,C))
        & v1_midsp_1(k8_midsp_2(A,B,C))
        & v2_midsp_1(k8_midsp_2(A,B,C))
        & l1_midsp_1(k8_midsp_2(A,B,C)) ) ) )).

fof(dt_k9_midsp_2,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(A)
        & v2_midsp_1(A)
        & l1_midsp_1(A)
        & l1_midsp_2(B,A)
        & m1_subset_1(C,u1_struct_0(A))
        & m1_subset_1(D,u1_struct_0(A)) )
     => m1_subset_1(k9_midsp_2(A,B,C,D),u1_struct_0(u1_midsp_2(A,B))) ) )).

fof(dt_k10_midsp_2,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(A)
        & v2_midsp_1(A)
        & l1_midsp_1(A)
        & l1_midsp_2(B,A)
        & m1_subset_1(C,u1_struct_0(A))
        & m1_subset_1(D,u1_struct_0(u1_midsp_2(A,B))) )
     => m1_subset_1(k10_midsp_2(A,B,C,D),u1_struct_0(A)) ) )).

fof(dt_k11_midsp_2,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_midsp_1(A)
        & l1_midsp_1(A)
        & v3_midsp_2(B,A)
        & l1_midsp_2(B,A) )
     => m1_subset_1(k11_midsp_2(A,B),u1_struct_0(u1_midsp_2(A,B))) ) )).

fof(dt_u1_midsp_2,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_midsp_1(A)
        & l1_midsp_2(B,A) )
     => ( ~ v3_struct_0(u1_midsp_2(A,B))
        & l1_rlvect_1(u1_midsp_2(A,B)) ) ) )).

fof(dt_u2_midsp_2,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_midsp_1(A)
        & l1_midsp_2(B,A) )
     => ( v1_funct_1(u2_midsp_2(A,B))
        & v1_funct_2(u2_midsp_2(A,B),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(u1_midsp_2(A,B)))
        & m2_relset_1(u2_midsp_2(A,B),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(u1_midsp_2(A,B))) ) ) )).

fof(dt_g1_midsp_2,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_midsp_1(A)
        & ~ v3_struct_0(B)
        & l1_rlvect_1(B)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(B))
        & m1_relset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(B)) )
     => ( v2_midsp_2(g1_midsp_2(A,B,C),A)
        & l1_midsp_2(g1_midsp_2(A,B,C),A) ) ) )).

fof(free_g1_midsp_2,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_midsp_1(A)
        & ~ v3_struct_0(B)
        & l1_rlvect_1(B)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(B))
        & m1_relset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(B)) )
     => ! [D,E,F] :
          ( g1_midsp_2(A,B,C) = g1_midsp_2(D,E,F)
         => ( A = D
            & B = E
            & C = F ) ) ) )).
%------------------------------------------------------------------------------