SET007 Axioms: SET007+337.ax


%------------------------------------------------------------------------------
% File     : SET007+337 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Reper Algebras
% 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_3 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   80 (   3 unit)
%            Number of atoms       :  667 ( 104 equality)
%            Maximal formula depth :   25 (  12 average)
%            Number of connectives :  647 (  60 ~  ;   0  |; 221  &)
%                                         (  21 <=>; 345 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   27 (   1 propositional; 0-3 arity)
%            Number of functors    :   43 (   6 constant; 0-6 arity)
%            Number of variables   :  382 (   0 singleton; 375 !;   7 ?)
%            Maximal term depth    :    7 (   1 average)
% SPC      : 

% Comments : The individual reference can be found in [Mat90] by looking for
%            the name provided by [Urb08].
%          : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
%          : These set theory axioms are used in encodings of problems in
%            various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(rc1_midsp_3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k5_numbers)
     => ? [B] :
          ( l1_midsp_3(B,A)
          & v1_midsp_3(B,A) ) ) )).

fof(fc1_midsp_3,axiom,(
    ! [A,B,C,D] :
      ( ( m1_subset_1(A,k5_numbers)
        & ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(B,B),B)
        & m1_relset_1(C,k2_zfmisc_1(B,B),B)
        & v1_funct_1(D)
        & v1_funct_2(D,k4_finseq_2(A,B),B)
        & m1_relset_1(D,k4_finseq_2(A,B),B) )
     => ( ~ v3_struct_0(g1_midsp_3(A,B,C,D))
        & v1_midsp_3(g1_midsp_3(A,B,C,D),A) ) ) )).

fof(rc2_midsp_3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k5_numbers)
     => ? [B] :
          ( l1_midsp_3(B,A)
          & ~ v3_struct_0(B) ) ) )).

fof(rc3_midsp_3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k5_numbers)
     => ? [B] :
          ( l1_midsp_3(B,k1_nat_1(A,np__2))
          & ~ v3_struct_0(B)
          & v2_midsp_1(B) ) ) )).

fof(t1_midsp_3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( m2_finseq_1(D,C)
                 => ~ ( k3_finseq_1(D) = k1_nat_1(k1_nat_1(A,np__1),B)
                      & ! [E] :
                          ( m2_finseq_1(E,C)
                         => ! [F] :
                              ( m2_finseq_1(F,C)
                             => ! [G] :
                                  ( m1_subset_1(G,C)
                                 => ~ ( k3_finseq_1(E) = A
                                      & k3_finseq_1(F) = B
                                      & D = k8_finseq_1(C,k8_finseq_1(C,E,k12_finseq_1(C,G)),F) ) ) ) ) ) ) ) ) ) )).

fof(t2_midsp_3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ~ ( r2_hidden(A,k2_finseq_1(B))
              & ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ! [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ~ ( B = k1_nat_1(k1_nat_1(C,np__1),D)
                          & A = k1_nat_1(C,np__1) ) ) ) ) ) ) )).

fof(t3_midsp_3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m1_subset_1(C,B)
             => ! [D] :
                  ( m2_finseq_1(D,B)
                 => ! [E] :
                      ( m2_finseq_1(E,B)
                     => ! [F] :
                          ( m2_finseq_1(F,B)
                         => ( ( D = k8_finseq_1(B,k8_finseq_1(B,E,k12_finseq_1(B,C)),F)
                              & A = k1_nat_1(k3_finseq_1(E),np__1) )
                           => ( ! [G] :
                                  ( m2_subset_1(G,k1_numbers,k5_numbers)
                                 => ( ( r1_xreal_0(np__1,G)
                                      & r1_xreal_0(G,k3_finseq_1(E)) )
                                   => k1_funct_1(D,G) = k1_funct_1(E,G) ) )
                              & k1_funct_1(D,A) = C
                              & ! [G] :
                                  ( m2_subset_1(G,k1_numbers,k5_numbers)
                                 => ( ( r1_xreal_0(k1_nat_1(A,np__1),G)
                                      & r1_xreal_0(G,k3_finseq_1(D)) )
                                   => k1_funct_1(D,G) = k1_funct_1(F,k6_xcmplx_0(G,A)) ) ) ) ) ) ) ) ) ) ) )).

fof(t4_midsp_3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ~ ( ~ r1_xreal_0(A,B)
              & A != k1_nat_1(B,np__1)
              & ~ r1_xreal_0(k1_nat_1(B,np__2),A) ) ) ) )).

fof(t5_midsp_3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ~ ( r2_hidden(A,k4_xboole_0(k2_finseq_1(B),k1_tarski(C)))
                      & C = k1_nat_1(D,np__1)
                      & ~ ( r1_xreal_0(np__1,A)
                          & r1_xreal_0(A,D) )
                      & ~ ( r1_xreal_0(k1_nat_1(C,np__1),A)
                          & r1_xreal_0(A,B) ) ) ) ) ) ) )).

fof(d1_midsp_3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( m1_subset_1(D,C)
                 => ! [E] :
                      ( m2_finseq_2(E,C,k4_finseq_2(A,C))
                     => ( r2_hidden(B,k2_finseq_1(A))
                       => ! [F] :
                            ( m2_finseq_2(F,C,k4_finseq_2(A,C))
                           => ( F = k1_midsp_3(A,B,C,D,E)
                            <=> ( k1_funct_1(F,B) = D
                                & ! [G] :
                                    ( m2_subset_1(G,k1_numbers,k5_numbers)
                                   => ( r2_hidden(G,k4_xboole_0(k4_finseq_1(E),k1_tarski(B)))
                                     => k1_funct_1(F,G) = k1_funct_1(E,G) ) ) ) ) ) ) ) ) ) ) ) )).

fof(d2_midsp_3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_midsp_1(B)
            & l1_midsp_3(B,k1_nat_1(A,np__2)) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m2_finseq_2(D,u1_struct_0(B),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(B)))
                 => k4_midsp_3(A,B,C,D) = k1_funct_1(u1_midsp_3(k1_nat_1(A,np__2),B),k3_midsp_3(A,B,np__1,k1_nat_1(A,np__1),k2_midsp_3(A,B,C),D)) ) ) ) ) )).

fof(d3_midsp_3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v2_midsp_1(C)
                & l1_midsp_3(C,k1_nat_1(A,np__2)) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(C))
                 => ! [E] :
                      ( m2_finseq_2(E,u1_struct_0(C),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(C)))
                     => ! [F] :
                          ( m2_finseq_2(F,u1_struct_0(C),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(C)))
                         => ( F = k5_midsp_3(A,B,C,D,E)
                          <=> ! [G] :
                                ( ~ v1_xboole_0(G)
                               => ! [H] :
                                    ( m2_finseq_2(H,G,k4_finseq_2(k1_nat_1(A,np__1),G))
                                   => ! [I] :
                                        ( m1_subset_1(I,G)
                                       => ( ( G = u1_struct_0(C)
                                            & H = E
                                            & I = D )
                                         => F = k1_midsp_3(k1_nat_1(A,np__1),B,G,I,H) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t6_midsp_3,axiom,(
    $true )).

fof(t7_midsp_3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v2_midsp_1(C)
                & l1_midsp_3(C,k1_nat_1(B,np__2)) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(C))
                 => ! [E] :
                      ( m2_finseq_2(E,u1_struct_0(C),k4_finseq_2(k1_nat_1(B,np__1),u1_struct_0(C)))
                     => ( r2_hidden(A,k2_finseq_1(k1_nat_1(B,np__1)))
                       => ( k1_funct_1(k5_midsp_3(B,A,C,D,E),A) = D
                          & ! [F] :
                              ( m2_subset_1(F,k1_numbers,k5_numbers)
                             => ( r2_hidden(F,k4_xboole_0(k4_finseq_1(E),k1_tarski(A)))
                               => k1_funct_1(k5_midsp_3(B,A,C,D,E),F) = k1_funct_1(E,F) ) ) ) ) ) ) ) ) ) )).

fof(d4_midsp_3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( m1_midsp_3(B,A)
          <=> ( r1_xreal_0(np__1,B)
              & r1_xreal_0(B,k1_nat_1(A,np__1)) ) ) ) ) )).

fof(t8_midsp_3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( m1_midsp_3(A,B)
          <=> r2_hidden(A,k2_finseq_1(k1_nat_1(B,np__1))) ) ) ) )).

fof(t9_midsp_3,axiom,(
    $true )).

fof(t10_midsp_3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( r1_xreal_0(A,B)
           => m1_midsp_3(k1_nat_1(A,np__1),B) ) ) ) )).

fof(t11_midsp_3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_midsp_1(B)
            & l1_midsp_3(B,k1_nat_1(A,np__2)) )
         => ! [C] :
              ( m2_finseq_2(C,u1_struct_0(B),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(B)))
             => ! [D] :
                  ( m2_finseq_2(D,u1_struct_0(B),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(B)))
                 => ( ! [E] :
                        ( m1_midsp_3(E,A)
                       => k1_funct_1(C,E) = k1_funct_1(D,E) )
                   => C = D ) ) ) ) ) )).

fof(t12_midsp_3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v2_midsp_1(C)
                & l1_midsp_3(C,k1_nat_1(A,np__2)) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(C))
                 => ! [E] :
                      ( m2_finseq_2(E,u1_struct_0(C),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(C)))
                     => ( ! [F] :
                            ( m1_midsp_3(F,A)
                           => ( F = B
                             => k1_funct_1(k5_midsp_3(A,B,C,D,E),F) = D ) )
                        & ! [F] :
                            ( m1_midsp_3(F,A)
                           => ! [G] :
                                ( m1_midsp_3(G,A)
                               => ( F != G
                                 => k1_funct_1(k5_midsp_3(A,G,C,D,E),F) = k1_funct_1(E,F) ) ) ) ) ) ) ) ) ) )).

fof(d5_midsp_3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_midsp_1(B)
            & l1_midsp_3(B,k1_nat_1(A,np__2)) )
         => ( v2_midsp_3(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,u1_struct_0(B))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(B))
                   => ! [E] :
                        ( m2_finseq_2(E,u1_struct_0(B),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(B)))
                       => ! [F] :
                            ( m2_finseq_2(F,u1_struct_0(B),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(B)))
                           => ( ! [G] :
                                  ( m1_midsp_3(G,A)
                                 => k4_midsp_1(B,C,k6_midsp_3(A,u1_struct_0(B),F,G)) = k4_midsp_1(B,D,k6_midsp_3(A,u1_struct_0(B),E,G)) )
                             => k4_midsp_1(B,C,k4_midsp_3(A,B,D,F)) = k4_midsp_1(B,D,k4_midsp_3(A,B,C,E)) ) ) ) ) ) ) ) ) )).

fof(d6_midsp_3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v2_midsp_1(C)
                & l1_midsp_3(C,k1_nat_1(A,np__2)) )
             => ( r1_midsp_3(A,B,C)
              <=> ! [D] :
                    ( m1_subset_1(D,u1_struct_0(C))
                   => ! [E] :
                        ( m2_finseq_2(E,u1_struct_0(C),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(C)))
                       => k4_midsp_3(A,C,D,k5_midsp_3(A,B,C,D,E)) = D ) ) ) ) ) ) )).

fof(d7_midsp_3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v2_midsp_1(C)
                & l1_midsp_3(C,k1_nat_1(A,np__2)) )
             => ( r2_midsp_3(A,B,C)
              <=> ! [D] :
                    ( m1_subset_1(D,u1_struct_0(C))
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(C))
                       => ! [F] :
                            ( m2_finseq_2(F,u1_struct_0(C),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(C)))
                           => ( k1_funct_1(F,B) = E
                             => k4_midsp_3(A,C,D,k5_midsp_3(A,B,C,k4_midsp_1(C,D,E),F)) = k4_midsp_1(C,D,k4_midsp_3(A,C,D,F)) ) ) ) ) ) ) ) ) )).

fof(t13_midsp_3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_midsp_1(B)
            & l1_midsp_3(B,k1_nat_1(A,np__2)) )
         => ! [C] :
              ( m1_midsp_3(C,A)
             => ( r2_midsp_3(A,C,B)
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(B))
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(B))
                       => ! [F] :
                            ( m2_finseq_2(F,u1_struct_0(B),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(B)))
                           => ! [G] :
                                ( m2_finseq_2(G,u1_struct_0(B),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(B)))
                               => ( G = k5_midsp_3(A,C,B,E,F)
                                 => k4_midsp_3(A,B,D,k5_midsp_3(A,C,B,k4_midsp_1(B,D,E),F)) = k4_midsp_1(B,D,k4_midsp_3(A,B,D,G)) ) ) ) ) ) ) ) ) ) )).

fof(d8_midsp_3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v2_midsp_1(C)
                & l1_midsp_3(C,k1_nat_1(A,np__2)) )
             => ( r3_midsp_3(A,B,C)
              <=> ! [D] :
                    ( m1_subset_1(D,u1_struct_0(C))
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(C))
                       => ! [F] :
                            ( m1_subset_1(F,u1_struct_0(C))
                           => ! [G] :
                                ( m2_finseq_2(G,u1_struct_0(C),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(C)))
                               => ( k1_funct_1(G,B) = E
                                 => k4_midsp_3(A,C,D,k5_midsp_3(A,B,C,k4_midsp_1(C,E,F),G)) = k4_midsp_1(C,k4_midsp_3(A,C,D,G),k4_midsp_3(A,C,D,k5_midsp_3(A,B,C,F,G))) ) ) ) ) ) ) ) ) ) )).

fof(d9_midsp_3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v2_midsp_1(C)
                & l1_midsp_3(C,k1_nat_1(A,np__2)) )
             => ( r4_midsp_3(A,B,C)
              <=> ! [D] :
                    ( m1_subset_1(D,u1_struct_0(C))
                   => ! [E] :
                        ( m2_finseq_2(E,u1_struct_0(C),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(C)))
                       => ! [F] :
                            ( m1_subset_1(F,u1_struct_0(C))
                           => ( k1_funct_1(E,B) = F
                             => k4_midsp_3(A,C,D,k5_midsp_3(A,k1_nat_1(B,np__1),C,F,E)) = D ) ) ) ) ) ) ) ) )).

fof(d10_midsp_3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_midsp_1(B)
            & l1_midsp_3(B,k1_nat_1(A,np__2)) )
         => ! [C] :
              ( ( v3_midsp_2(C,B)
                & l1_midsp_2(C,B) )
             => ! [D] :
                  ( m2_finseq_2(D,u1_struct_0(u1_midsp_2(B,C)),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(u1_midsp_2(B,C))))
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(u1_midsp_2(B,C)))
                         => ! [G] :
                              ( m2_finseq_2(G,u1_struct_0(u1_midsp_2(B,C)),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(u1_midsp_2(B,C))))
                             => ( G = k7_midsp_3(A,B,C,D,E,F)
                              <=> ! [H] :
                                    ( ~ v1_xboole_0(H)
                                   => ! [I] :
                                        ( m2_finseq_2(I,H,k4_finseq_2(k1_nat_1(A,np__1),H))
                                       => ! [J] :
                                            ( m1_subset_1(J,H)
                                           => ( ( H = u1_struct_0(u1_midsp_2(B,C))
                                                & I = D
                                                & J = F )
                                             => G = k1_midsp_3(k1_nat_1(A,np__1),E,H,J,I) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t14_midsp_3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v2_midsp_1(C)
                & l1_midsp_3(C,k1_nat_1(B,np__2)) )
             => ! [D] :
                  ( ( v3_midsp_2(D,C)
                    & l1_midsp_2(D,C) )
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(u1_midsp_2(C,D)))
                     => ! [F] :
                          ( m2_finseq_2(F,u1_struct_0(u1_midsp_2(C,D)),k4_finseq_2(k1_nat_1(B,np__1),u1_struct_0(u1_midsp_2(C,D))))
                         => ( r2_hidden(A,k2_finseq_1(k1_nat_1(B,np__1)))
                           => ( k1_funct_1(k7_midsp_3(B,C,D,F,A,E),A) = E
                              & ! [G] :
                                  ( m2_subset_1(G,k1_numbers,k5_numbers)
                                 => ( r2_hidden(G,k4_xboole_0(k4_finseq_1(F),k1_tarski(A)))
                                   => k1_funct_1(k7_midsp_3(B,C,D,F,A,E),G) = k1_funct_1(F,G) ) ) ) ) ) ) ) ) ) ) )).

fof(t15_midsp_3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v2_midsp_1(C)
                & l1_midsp_3(C,k1_nat_1(A,np__2)) )
             => ! [D] :
                  ( ( v3_midsp_2(D,C)
                    & l1_midsp_2(D,C) )
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(u1_midsp_2(C,D)))
                     => ! [F] :
                          ( m2_finseq_2(F,u1_struct_0(u1_midsp_2(C,D)),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(u1_midsp_2(C,D))))
                         => ( ! [G] :
                                ( m1_midsp_3(G,A)
                               => ( G = B
                                 => k6_midsp_3(A,u1_struct_0(u1_midsp_2(C,D)),k7_midsp_3(A,C,D,F,B,E),G) = E ) )
                            & ! [G] :
                                ( m1_midsp_3(G,A)
                               => ! [H] :
                                    ( m1_midsp_3(H,A)
                                   => ( G != H
                                     => k6_midsp_3(A,u1_struct_0(u1_midsp_2(C,D)),k7_midsp_3(A,C,D,F,H,E),G) = k6_midsp_3(A,u1_struct_0(u1_midsp_2(C,D)),F,G) ) ) ) ) ) ) ) ) ) ) )).

fof(t16_midsp_3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_midsp_1(B)
            & l1_midsp_3(B,k1_nat_1(A,np__2)) )
         => ! [C] :
              ( ( v3_midsp_2(C,B)
                & l1_midsp_2(C,B) )
             => ! [D] :
                  ( m2_finseq_2(D,u1_struct_0(u1_midsp_2(B,C)),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(u1_midsp_2(B,C))))
                 => ! [E] :
                      ( m2_finseq_2(E,u1_struct_0(u1_midsp_2(B,C)),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(u1_midsp_2(B,C))))
                     => ( ! [F] :
                            ( m1_midsp_3(F,A)
                           => k6_midsp_3(A,u1_struct_0(u1_midsp_2(B,C)),D,F) = k6_midsp_3(A,u1_struct_0(u1_midsp_2(B,C)),E,F) )
                       => D = E ) ) ) ) ) ) )).

fof(d11_midsp_3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_midsp_1(B)
            & l1_midsp_3(B,k1_nat_1(A,np__2)) )
         => ! [C] :
              ( ( v3_midsp_2(C,B)
                & l1_midsp_2(C,B) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ! [E] :
                      ( m2_finseq_2(E,u1_struct_0(u1_midsp_2(B,C)),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(u1_midsp_2(B,C))))
                     => ! [F] :
                          ( m2_finseq_2(F,u1_struct_0(B),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(B)))
                         => ( F = k8_midsp_3(A,B,C,D,E)
                          <=> ! [G] :
                                ( m1_midsp_3(G,A)
                               => k6_midsp_3(A,u1_struct_0(B),F,G) = k10_midsp_2(B,C,D,k6_midsp_3(A,u1_struct_0(u1_midsp_2(B,C)),E,G)) ) ) ) ) ) ) ) ) )).

fof(d12_midsp_3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_midsp_1(B)
            & l1_midsp_3(B,k1_nat_1(A,np__2)) )
         => ! [C] :
              ( ( v3_midsp_2(C,B)
                & l1_midsp_2(C,B) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ! [E] :
                      ( m2_finseq_2(E,u1_struct_0(B),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(B)))
                     => ! [F] :
                          ( m2_finseq_2(F,u1_struct_0(u1_midsp_2(B,C)),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(u1_midsp_2(B,C))))
                         => ( F = k9_midsp_3(A,B,C,D,E)
                          <=> ! [G] :
                                ( m1_midsp_3(G,A)
                               => k6_midsp_3(A,u1_struct_0(u1_midsp_2(B,C)),F,G) = k9_midsp_2(B,C,D,k6_midsp_3(A,u1_struct_0(B),E,G)) ) ) ) ) ) ) ) ) )).

fof(t17_midsp_3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_midsp_1(B)
            & l1_midsp_3(B,k1_nat_1(A,np__2)) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m2_finseq_2(D,u1_struct_0(B),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(B)))
                 => ! [E] :
                      ( ( v3_midsp_2(E,B)
                        & l1_midsp_2(E,B) )
                     => ! [F] :
                          ( m2_finseq_2(F,u1_struct_0(u1_midsp_2(B,E)),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(u1_midsp_2(B,E))))
                         => ( k9_midsp_3(A,B,E,C,D) = F
                          <=> k8_midsp_3(A,B,E,C,F) = D ) ) ) ) ) ) ) )).

fof(t18_midsp_3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_midsp_1(B)
            & l1_midsp_3(B,k1_nat_1(A,np__2)) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( ( v3_midsp_2(D,B)
                    & l1_midsp_2(D,B) )
                 => ! [E] :
                      ( m2_finseq_2(E,u1_struct_0(u1_midsp_2(B,D)),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(u1_midsp_2(B,D))))
                     => k9_midsp_3(A,B,D,C,k8_midsp_3(A,B,D,C,E)) = E ) ) ) ) ) )).

fof(t19_midsp_3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_midsp_1(B)
            & l1_midsp_3(B,k1_nat_1(A,np__2)) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m2_finseq_2(D,u1_struct_0(B),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(B)))
                 => ! [E] :
                      ( ( v3_midsp_2(E,B)
                        & l1_midsp_2(E,B) )
                     => k8_midsp_3(A,B,E,C,k9_midsp_3(A,B,E,C,D)) = D ) ) ) ) ) )).

fof(d13_midsp_3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_midsp_1(B)
            & l1_midsp_3(B,k1_nat_1(A,np__2)) )
         => ! [C] :
              ( ( v3_midsp_2(C,B)
                & l1_midsp_2(C,B) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ! [E] :
                      ( m2_finseq_2(E,u1_struct_0(u1_midsp_2(B,C)),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(u1_midsp_2(B,C))))
                     => k10_midsp_3(A,B,C,D,E) = k9_midsp_2(B,C,D,k4_midsp_3(A,B,D,k8_midsp_3(A,B,C,D,E))) ) ) ) ) ) )).

fof(t20_midsp_3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_midsp_1(B)
            & l1_midsp_3(B,k1_nat_1(A,np__2)) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ! [E] :
                      ( m2_finseq_2(E,u1_struct_0(B),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(B)))
                     => ! [F] :
                          ( ( v3_midsp_2(F,B)
                            & l1_midsp_2(F,B) )
                         => ! [G] :
                              ( m1_subset_1(G,u1_struct_0(u1_midsp_2(B,F)))
                             => ! [H] :
                                  ( m2_finseq_2(H,u1_struct_0(u1_midsp_2(B,F)),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(u1_midsp_2(B,F))))
                                 => ( ( k9_midsp_3(A,B,F,C,E) = H
                                      & k9_midsp_2(B,F,C,D) = G )
                                   => ( k4_midsp_3(A,B,C,E) = D
                                    <=> k10_midsp_3(A,B,F,C,H) = G ) ) ) ) ) ) ) ) ) ) )).

fof(t21_midsp_3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_midsp_1(B)
            & l1_midsp_3(B,k1_nat_1(A,np__2)) )
         => ! [C] :
              ( ( v3_midsp_2(C,B)
                & l1_midsp_2(C,B) )
             => ( v2_midsp_3(B,A)
              <=> ! [D] :
                    ( m1_subset_1(D,u1_struct_0(B))
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(B))
                       => ! [F] :
                            ( m2_finseq_2(F,u1_struct_0(u1_midsp_2(B,C)),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(u1_midsp_2(B,C))))
                           => k10_midsp_3(A,B,C,D,F) = k10_midsp_3(A,B,C,E,F) ) ) ) ) ) ) ) )).

fof(t22_midsp_3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => r2_hidden(np__1,k2_finseq_1(k1_nat_1(A,np__1))) ) )).

fof(t23_midsp_3,axiom,(
    $true )).

fof(t24_midsp_3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => m1_midsp_3(np__1,A) ) )).

fof(d14_midsp_3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_midsp_1(B)
            & l1_midsp_3(B,k1_nat_1(A,np__2)) )
         => ( m2_midsp_3(B,A)
          <=> v2_midsp_3(B,A) ) ) ) )).

fof(t25_midsp_3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_midsp_3(B,A)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ! [E] :
                      ( ( v3_midsp_2(E,B)
                        & l1_midsp_2(E,B) )
                     => ! [F] :
                          ( m2_finseq_2(F,u1_struct_0(u1_midsp_2(B,E)),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(u1_midsp_2(B,E))))
                         => k10_midsp_3(A,B,E,C,F) = k10_midsp_3(A,B,E,D,F) ) ) ) ) ) ) )).

fof(d15_midsp_3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_midsp_3(B,A)
         => ! [C] :
              ( ( v3_midsp_2(C,B)
                & l1_midsp_2(C,B) )
             => ! [D] :
                  ( m2_finseq_2(D,u1_struct_0(u1_midsp_2(B,C)),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(u1_midsp_2(B,C))))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(u1_midsp_2(B,C)))
                     => ( E = k11_midsp_3(A,B,C,D)
                      <=> ! [F] :
                            ( m1_subset_1(F,u1_struct_0(B))
                           => E = k10_midsp_3(A,B,C,F,D) ) ) ) ) ) ) ) )).

fof(t26_midsp_3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_midsp_3(B,A)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ! [E] :
                      ( m2_finseq_2(E,u1_struct_0(B),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(B)))
                     => ! [F] :
                          ( ( v3_midsp_2(F,B)
                            & l1_midsp_2(F,B) )
                         => ! [G] :
                              ( m1_subset_1(G,u1_struct_0(u1_midsp_2(B,F)))
                             => ! [H] :
                                  ( m2_finseq_2(H,u1_struct_0(u1_midsp_2(B,F)),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(u1_midsp_2(B,F))))
                                 => ( ( k9_midsp_3(A,B,F,C,E) = H
                                      & k9_midsp_2(B,F,C,D) = G
                                      & k11_midsp_3(A,B,F,H) = G )
                                   => k4_midsp_3(A,B,C,E) = D ) ) ) ) ) ) ) ) ) )).

fof(t27_midsp_3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_midsp_3(B,A)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ! [E] :
                      ( m2_finseq_2(E,u1_struct_0(B),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(B)))
                     => ! [F] :
                          ( ( v3_midsp_2(F,B)
                            & l1_midsp_2(F,B) )
                         => ! [G] :
                              ( m1_subset_1(G,u1_struct_0(u1_midsp_2(B,F)))
                             => ! [H] :
                                  ( m2_finseq_2(H,u1_struct_0(u1_midsp_2(B,F)),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(u1_midsp_2(B,F))))
                                 => ( ( k8_midsp_3(A,B,F,C,H) = E
                                      & k10_midsp_2(B,F,C,G) = D
                                      & k4_midsp_3(A,B,C,E) = D )
                                   => k11_midsp_3(A,B,F,H) = G ) ) ) ) ) ) ) ) ) )).

fof(t28_midsp_3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_midsp_3(B,A)
         => ! [C] :
              ( m2_midsp_3(C,A)
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(C))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(C))
                     => ! [F] :
                          ( m2_finseq_2(F,u1_struct_0(C),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(C)))
                         => ! [G] :
                              ( ( v3_midsp_2(G,C)
                                & l1_midsp_2(G,C) )
                             => ! [H] :
                                  ( m1_subset_1(H,u1_struct_0(u1_midsp_2(C,G)))
                                 => ! [I] :
                                      ( m2_finseq_2(I,u1_struct_0(u1_midsp_2(C,G)),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(u1_midsp_2(C,G))))
                                     => ( ( k9_midsp_3(A,C,G,D,F) = I
                                          & k9_midsp_2(C,G,D,E) = H )
                                       => k9_midsp_3(A,C,G,D,k5_midsp_3(A,B,C,E,F)) = k7_midsp_3(A,C,G,I,B,H) ) ) ) ) ) ) ) ) ) ) )).

fof(t29_midsp_3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_midsp_3(B,A)
         => ! [C] :
              ( m2_midsp_3(C,A)
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(C))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(C))
                     => ! [F] :
                          ( m2_finseq_2(F,u1_struct_0(C),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(C)))
                         => ! [G] :
                              ( ( v3_midsp_2(G,C)
                                & l1_midsp_2(G,C) )
                             => ! [H] :
                                  ( m1_subset_1(H,u1_struct_0(u1_midsp_2(C,G)))
                                 => ! [I] :
                                      ( m2_finseq_2(I,u1_struct_0(u1_midsp_2(C,G)),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(u1_midsp_2(C,G))))
                                     => ( ( k8_midsp_3(A,C,G,D,I) = F
                                          & k10_midsp_2(C,G,D,H) = E )
                                       => k8_midsp_3(A,C,G,D,k7_midsp_3(A,C,G,I,B,H)) = k5_midsp_3(A,B,C,E,F) ) ) ) ) ) ) ) ) ) ) )).

fof(t30_midsp_3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_midsp_3(B,A)
         => ! [C] :
              ( m2_midsp_3(C,A)
             => ! [D] :
                  ( ( v3_midsp_2(D,C)
                    & l1_midsp_2(D,C) )
                 => ( r1_midsp_3(A,B,C)
                  <=> ! [E] :
                        ( m2_finseq_2(E,u1_struct_0(u1_midsp_2(C,D)),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(u1_midsp_2(C,D))))
                       => k11_midsp_3(A,C,D,k7_midsp_3(A,C,D,E,B,k11_midsp_2(C,D))) = k11_midsp_2(C,D) ) ) ) ) ) ) )).

fof(t31_midsp_3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_midsp_3(B,A)
         => ! [C] :
              ( m2_midsp_3(C,A)
             => ! [D] :
                  ( ( v3_midsp_2(D,C)
                    & l1_midsp_2(D,C) )
                 => ( r2_midsp_3(A,B,C)
                  <=> ! [E] :
                        ( m2_finseq_2(E,u1_struct_0(u1_midsp_2(C,D)),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(u1_midsp_2(C,D))))
                       => k11_midsp_3(A,C,D,k7_midsp_3(A,C,D,E,B,k1_midsp_2(u1_midsp_2(C,D),k6_midsp_3(A,u1_struct_0(u1_midsp_2(C,D)),E,B)))) = k1_midsp_2(u1_midsp_2(C,D),k11_midsp_3(A,C,D,E)) ) ) ) ) ) ) )).

fof(t32_midsp_3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_midsp_3(B,A)
         => ! [C] :
              ( m2_midsp_3(C,A)
             => ( ( r1_midsp_3(A,B,C)
                  & r3_midsp_3(A,B,C) )
               => r2_midsp_3(A,B,C) ) ) ) ) )).

fof(t33_midsp_3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_midsp_3(B,A)
         => ! [C] :
              ( m2_midsp_3(C,A)
             => ! [D] :
                  ( ( v3_midsp_2(D,C)
                    & l1_midsp_2(D,C) )
                 => ( r1_midsp_3(A,B,C)
                   => ( r3_midsp_3(A,B,C)
                    <=> ! [E] :
                          ( m2_finseq_2(E,u1_struct_0(u1_midsp_2(C,D)),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(u1_midsp_2(C,D))))
                         => ! [F] :
                              ( m1_subset_1(F,u1_struct_0(u1_midsp_2(C,D)))
                             => k11_midsp_3(A,C,D,k7_midsp_3(A,C,D,E,B,k2_rlvect_1(u1_midsp_2(C,D),k6_midsp_3(A,u1_struct_0(u1_midsp_2(C,D)),E,B),F))) = k2_rlvect_1(u1_midsp_2(C,D),k11_midsp_3(A,C,D,E),k11_midsp_3(A,C,D,k7_midsp_3(A,C,D,E,B,F))) ) ) ) ) ) ) ) ) )).

fof(t34_midsp_3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_midsp_3(B,A)
         => ! [C] :
              ( m2_midsp_3(C,A)
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(C))
                 => ! [E] :
                      ( m2_finseq_2(E,u1_struct_0(C),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(C)))
                     => ! [F] :
                          ( ( v3_midsp_2(F,C)
                            & l1_midsp_2(F,C) )
                         => ! [G] :
                              ( m2_finseq_2(G,u1_struct_0(u1_midsp_2(C,F)),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(u1_midsp_2(C,F))))
                             => ( ( k9_midsp_3(A,C,F,D,E) = G
                                  & r1_xreal_0(B,A) )
                               => k9_midsp_3(A,C,F,D,k5_midsp_3(A,k1_nat_1(B,np__1),C,k6_midsp_3(A,u1_struct_0(C),E,B),E)) = k7_midsp_3(A,C,F,G,k1_nat_1(B,np__1),k6_midsp_3(A,u1_struct_0(u1_midsp_2(C,F)),G,B)) ) ) ) ) ) ) ) ) )).

fof(t35_midsp_3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_midsp_3(B,A)
         => ! [C] :
              ( m2_midsp_3(C,A)
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(C))
                 => ! [E] :
                      ( m2_finseq_2(E,u1_struct_0(C),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(C)))
                     => ! [F] :
                          ( ( v3_midsp_2(F,C)
                            & l1_midsp_2(F,C) )
                         => ! [G] :
                              ( m2_finseq_2(G,u1_struct_0(u1_midsp_2(C,F)),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(u1_midsp_2(C,F))))
                             => ( ( k8_midsp_3(A,C,F,D,G) = E
                                  & r1_xreal_0(B,A) )
                               => k8_midsp_3(A,C,F,D,k7_midsp_3(A,C,F,G,k1_nat_1(B,np__1),k6_midsp_3(A,u1_struct_0(u1_midsp_2(C,F)),G,B))) = k5_midsp_3(A,k1_nat_1(B,np__1),C,k6_midsp_3(A,u1_struct_0(C),E,B),E) ) ) ) ) ) ) ) ) )).

fof(t36_midsp_3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_midsp_3(B,A)
         => ! [C] :
              ( m2_midsp_3(C,A)
             => ! [D] :
                  ( ( v3_midsp_2(D,C)
                    & l1_midsp_2(D,C) )
                 => ( r1_xreal_0(B,A)
                   => ( r4_midsp_3(A,B,C)
                    <=> ! [E] :
                          ( m2_finseq_2(E,u1_struct_0(u1_midsp_2(C,D)),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(u1_midsp_2(C,D))))
                         => k11_midsp_3(A,C,D,k7_midsp_3(A,C,D,E,k1_nat_1(B,np__1),k6_midsp_3(A,u1_struct_0(u1_midsp_2(C,D)),E,B))) = k11_midsp_2(C,D) ) ) ) ) ) ) ) )).

fof(s1_midsp_3,axiom,(
    ? [A] :
      ( m2_finseq_1(A,f2_s1_midsp_3)
      & k3_finseq_1(A) = k1_nat_1(f1_s1_midsp_3,np__1)
      & ! [B] :
          ( m1_midsp_3(B,f1_s1_midsp_3)
         => k1_funct_1(A,B) = f3_s1_midsp_3(B) ) ) )).

fof(dt_m1_midsp_3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k5_numbers)
     => ! [B] :
          ( m1_midsp_3(B,A)
         => m2_subset_1(B,k1_numbers,k5_numbers) ) ) )).

fof(existence_m1_midsp_3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k5_numbers)
     => ? [B] : m1_midsp_3(B,A) ) )).

fof(dt_m2_midsp_3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k5_numbers)
     => ! [B] :
          ( m2_midsp_3(B,A)
         => ( ~ v3_struct_0(B)
            & v2_midsp_1(B)
            & l1_midsp_3(B,k1_nat_1(A,np__2)) ) ) ) )).

fof(existence_m2_midsp_3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k5_numbers)
     => ? [B] : m2_midsp_3(B,A) ) )).

fof(dt_l1_midsp_3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k5_numbers)
     => ! [B] :
          ( l1_midsp_3(B,A)
         => l1_midsp_1(B) ) ) )).

fof(existence_l1_midsp_3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k5_numbers)
     => ? [B] : l1_midsp_3(B,A) ) )).

fof(abstractness_v1_midsp_3,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k5_numbers)
        & l1_midsp_3(B,A) )
     => ( v1_midsp_3(B,A)
       => B = g1_midsp_3(A,u1_struct_0(B),u1_midsp_1(B),u1_midsp_3(A,B)) ) ) )).

fof(dt_k1_midsp_3,axiom,(
    ! [A,B,C,D,E] :
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers)
        & ~ v1_xboole_0(C)
        & m1_subset_1(D,C)
        & m1_subset_1(E,k4_finseq_2(A,C)) )
     => m2_finseq_2(k1_midsp_3(A,B,C,D,E),C,k4_finseq_2(A,C)) ) )).

fof(dt_k2_midsp_3,axiom,(
    ! [A,B,C] :
      ( ( m1_subset_1(A,k5_numbers)
        & ~ v3_struct_0(B)
        & v2_midsp_1(B)
        & l1_midsp_3(B,k1_nat_1(A,np__2))
        & m1_subset_1(C,u1_struct_0(B)) )
     => m2_finseq_2(k2_midsp_3(A,B,C),u1_struct_0(B),k4_finseq_2(np__1,u1_struct_0(B))) ) )).

fof(redefinition_k2_midsp_3,axiom,(
    ! [A,B,C] :
      ( ( m1_subset_1(A,k5_numbers)
        & ~ v3_struct_0(B)
        & v2_midsp_1(B)
        & l1_midsp_3(B,k1_nat_1(A,np__2))
        & m1_subset_1(C,u1_struct_0(B)) )
     => k2_midsp_3(A,B,C) = k5_finseq_1(C) ) )).

fof(dt_k3_midsp_3,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( m1_subset_1(A,k5_numbers)
        & ~ v3_struct_0(B)
        & v2_midsp_1(B)
        & l1_midsp_3(B,k1_nat_1(A,np__2))
        & m1_subset_1(C,k5_numbers)
        & m1_subset_1(D,k5_numbers)
        & m1_subset_1(E,k4_finseq_2(C,u1_struct_0(B)))
        & m1_subset_1(F,k4_finseq_2(D,u1_struct_0(B))) )
     => m2_finseq_2(k3_midsp_3(A,B,C,D,E,F),u1_struct_0(B),k4_finseq_2(k1_nat_1(C,D),u1_struct_0(B))) ) )).

fof(redefinition_k3_midsp_3,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( m1_subset_1(A,k5_numbers)
        & ~ v3_struct_0(B)
        & v2_midsp_1(B)
        & l1_midsp_3(B,k1_nat_1(A,np__2))
        & m1_subset_1(C,k5_numbers)
        & m1_subset_1(D,k5_numbers)
        & m1_subset_1(E,k4_finseq_2(C,u1_struct_0(B)))
        & m1_subset_1(F,k4_finseq_2(D,u1_struct_0(B))) )
     => k3_midsp_3(A,B,C,D,E,F) = k7_finseq_1(E,F) ) )).

fof(dt_k4_midsp_3,axiom,(
    ! [A,B,C,D] :
      ( ( m1_subset_1(A,k5_numbers)
        & ~ v3_struct_0(B)
        & v2_midsp_1(B)
        & l1_midsp_3(B,k1_nat_1(A,np__2))
        & m1_subset_1(C,u1_struct_0(B))
        & m1_subset_1(D,k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(B))) )
     => m1_subset_1(k4_midsp_3(A,B,C,D),u1_struct_0(B)) ) )).

fof(dt_k5_midsp_3,axiom,(
    ! [A,B,C,D,E] :
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers)
        & ~ v3_struct_0(C)
        & v2_midsp_1(C)
        & l1_midsp_3(C,k1_nat_1(A,np__2))
        & m1_subset_1(D,u1_struct_0(C))
        & m1_subset_1(E,k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(C))) )
     => m2_finseq_2(k5_midsp_3(A,B,C,D,E),u1_struct_0(C),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(C))) ) )).

fof(dt_k6_midsp_3,axiom,(
    ! [A,B,C,D] :
      ( ( m1_subset_1(A,k5_numbers)
        & ~ v1_xboole_0(B)
        & m1_subset_1(C,k4_finseq_2(k1_nat_1(A,np__1),B))
        & m1_midsp_3(D,A) )
     => m1_subset_1(k6_midsp_3(A,B,C,D),B) ) )).

fof(redefinition_k6_midsp_3,axiom,(
    ! [A,B,C,D] :
      ( ( m1_subset_1(A,k5_numbers)
        & ~ v1_xboole_0(B)
        & m1_subset_1(C,k4_finseq_2(k1_nat_1(A,np__1),B))
        & m1_midsp_3(D,A) )
     => k6_midsp_3(A,B,C,D) = k1_funct_1(C,D) ) )).

fof(dt_k7_midsp_3,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( m1_subset_1(A,k5_numbers)
        & ~ v3_struct_0(B)
        & v2_midsp_1(B)
        & l1_midsp_3(B,k1_nat_1(A,np__2))
        & v3_midsp_2(C,B)
        & l1_midsp_2(C,B)
        & m1_subset_1(D,k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(u1_midsp_2(B,C))))
        & m1_subset_1(E,k5_numbers)
        & m1_subset_1(F,u1_struct_0(u1_midsp_2(B,C))) )
     => m2_finseq_2(k7_midsp_3(A,B,C,D,E,F),u1_struct_0(u1_midsp_2(B,C)),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(u1_midsp_2(B,C)))) ) )).

fof(dt_k8_midsp_3,axiom,(
    ! [A,B,C,D,E] :
      ( ( m1_subset_1(A,k5_numbers)
        & ~ v3_struct_0(B)
        & v2_midsp_1(B)
        & l1_midsp_3(B,k1_nat_1(A,np__2))
        & v3_midsp_2(C,B)
        & l1_midsp_2(C,B)
        & m1_subset_1(D,u1_struct_0(B))
        & m1_subset_1(E,k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(u1_midsp_2(B,C)))) )
     => m2_finseq_2(k8_midsp_3(A,B,C,D,E),u1_struct_0(B),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(B))) ) )).

fof(dt_k9_midsp_3,axiom,(
    ! [A,B,C,D,E] :
      ( ( m1_subset_1(A,k5_numbers)
        & ~ v3_struct_0(B)
        & v2_midsp_1(B)
        & l1_midsp_3(B,k1_nat_1(A,np__2))
        & v3_midsp_2(C,B)
        & l1_midsp_2(C,B)
        & m1_subset_1(D,u1_struct_0(B))
        & m1_subset_1(E,k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(B))) )
     => m2_finseq_2(k9_midsp_3(A,B,C,D,E),u1_struct_0(u1_midsp_2(B,C)),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(u1_midsp_2(B,C)))) ) )).

fof(dt_k10_midsp_3,axiom,(
    ! [A,B,C,D,E] :
      ( ( m1_subset_1(A,k5_numbers)
        & ~ v3_struct_0(B)
        & v2_midsp_1(B)
        & l1_midsp_3(B,k1_nat_1(A,np__2))
        & v3_midsp_2(C,B)
        & l1_midsp_2(C,B)
        & m1_subset_1(D,u1_struct_0(B))
        & m1_subset_1(E,k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(u1_midsp_2(B,C)))) )
     => m1_subset_1(k10_midsp_3(A,B,C,D,E),u1_struct_0(u1_midsp_2(B,C))) ) )).

fof(dt_k11_midsp_3,axiom,(
    ! [A,B,C,D] :
      ( ( m1_subset_1(A,k5_numbers)
        & m2_midsp_3(B,A)
        & v3_midsp_2(C,B)
        & l1_midsp_2(C,B)
        & m1_subset_1(D,k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(u1_midsp_2(B,C)))) )
     => m1_subset_1(k11_midsp_3(A,B,C,D),u1_struct_0(u1_midsp_2(B,C))) ) )).

fof(dt_u1_midsp_3,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k5_numbers)
        & l1_midsp_3(B,A) )
     => ( v1_funct_1(u1_midsp_3(A,B))
        & v1_funct_2(u1_midsp_3(A,B),k4_finseq_2(A,u1_struct_0(B)),u1_struct_0(B))
        & m2_relset_1(u1_midsp_3(A,B),k4_finseq_2(A,u1_struct_0(B)),u1_struct_0(B)) ) ) )).

fof(dt_g1_midsp_3,axiom,(
    ! [A,B,C,D] :
      ( ( m1_subset_1(A,k5_numbers)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(B,B),B)
        & m1_relset_1(C,k2_zfmisc_1(B,B),B)
        & v1_funct_1(D)
        & v1_funct_2(D,k4_finseq_2(A,B),B)
        & m1_relset_1(D,k4_finseq_2(A,B),B) )
     => ( v1_midsp_3(g1_midsp_3(A,B,C,D),A)
        & l1_midsp_3(g1_midsp_3(A,B,C,D),A) ) ) )).

fof(free_g1_midsp_3,axiom,(
    ! [A,B,C,D] :
      ( ( m1_subset_1(A,k5_numbers)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(B,B),B)
        & m1_relset_1(C,k2_zfmisc_1(B,B),B)
        & v1_funct_1(D)
        & v1_funct_2(D,k4_finseq_2(A,B),B)
        & m1_relset_1(D,k4_finseq_2(A,B),B) )
     => ! [E,F,G,H] :
          ( g1_midsp_3(A,B,C,D) = g1_midsp_3(E,F,G,H)
         => ( A = E
            & B = F
            & C = G
            & D = H ) ) ) )).
%------------------------------------------------------------------------------