% Mizar problem: t33_midsp_3,midsp_3,1031,10 
fof(t33_midsp_3,conjecture,(
    ! [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,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))) ) ) ) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_nat_1,cc1_relset_1,cc2_nat_1,cc3_nat_1,commutativity_k1_nat_1,commutativity_k2_xcmplx_0,commutativity_k4_midsp_1,d11_midsp_3,d12_midsp_3,d1_midsp_1,d2_midsp_3,d4_midsp_1,d8_midsp_3,dt_k10_midsp_2,dt_k11_midsp_2,dt_k11_midsp_3,dt_k1_binop_1,dt_k1_funct_1,dt_k1_midsp_1,dt_k1_nat_1,dt_k1_numbers,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_binop_1,dt_k2_midsp_3,dt_k2_rlvect_1,dt_k2_xcmplx_0,dt_k2_zfmisc_1,dt_k3_midsp_3,dt_k4_finseq_2,dt_k4_midsp_1,dt_k4_midsp_3,dt_k5_finseq_1,dt_k5_midsp_3,dt_k5_numbers,dt_k5_ordinal2,dt_k5_rlvect_1,dt_k6_midsp_3,dt_k7_finseq_1,dt_k7_midsp_3,dt_k8_midsp_3,dt_k9_midsp_2,dt_k9_midsp_3,dt_l1_midsp_1,dt_l1_midsp_2,dt_l1_midsp_3,dt_l1_rlvect_1,dt_l1_struct_0,dt_l2_struct_0,dt_m1_finseq_1,dt_m1_finseq_2,dt_m1_midsp_3,dt_m1_relset_1,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_finseq_2,dt_m2_midsp_3,dt_m2_relset_1,dt_m2_subset_1,dt_u1_midsp_1,dt_u1_midsp_2,dt_u1_midsp_3,dt_u1_struct_0,existence_l1_midsp_1,existence_l1_midsp_2,existence_l1_midsp_3,existence_l1_rlvect_1,existence_l1_struct_0,existence_l2_struct_0,existence_m1_finseq_1,existence_m1_finseq_2,existence_m1_midsp_3,existence_m1_relset_1,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_finseq_2,existence_m2_midsp_3,existence_m2_relset_1,existence_m2_subset_1,fc1_finseq_2,fc1_nat_1,fc1_struct_0,fc3_nat_1,fc4_nat_1,l42_midsp_3,l43_midsp_3,l51_midsp_3,l52_midsp_3,rc1_finseq_2,rc1_nat_1,rc2_midsp_3,rc2_nat_1,rc3_midsp_3,rc3_nat_1,rc3_struct_0,rc4_struct_0,rc5_struct_0,redefinition_k1_nat_1,redefinition_k2_binop_1,redefinition_k2_midsp_3,redefinition_k3_midsp_3,redefinition_k4_midsp_1,redefinition_k5_numbers,redefinition_k6_midsp_3,redefinition_m2_finseq_1,redefinition_m2_finseq_2,redefinition_m2_relset_1,redefinition_m2_subset_1,reflexivity_r1_tarski,spc1_boole,spc1_numerals,spc2_boole,spc2_numerals,t11_midsp_3,t12_midsp_3,t15_midsp_3,t17_midsp_3,t1_subset,t2_subset,t32_midsp_3,t36_midsp_2,t39_midsp_2,t3_subset,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole]),
    [file(midsp_3,t33_midsp_3)]).

fof(antisymmetry_r2_hidden,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => ~ r2_hidden(B,A) ) ),
    file(hidden,r2_hidden),
    []).

fof(cc1_nat_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A) ) ) ),
    file(nat_1,cc1_nat_1),
    []).

fof(cc1_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
     => v1_relat_1(C) ) ),
    file(relset_1,cc1_relset_1),
    []).

fof(cc2_nat_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A) ) ) ),
    file(nat_1,cc2_nat_1),
    []).

fof(cc3_nat_1,axiom,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ( v4_ordinal2(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A) ) ) ),
    file(nat_1,cc3_nat_1),
    []).

fof(commutativity_k1_nat_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers) )
     => k1_nat_1(A,B) = k1_nat_1(B,A) ) ),
    file(nat_1,k1_nat_1),
    []).

fof(commutativity_k2_xcmplx_0,axiom,(
    ! [A,B] : 
      ( ( v1_xcmplx_0(A)
        & v1_xcmplx_0(B) )
     => k2_xcmplx_0(A,B) = k2_xcmplx_0(B,A) ) ),
    file(xcmplx_0,k2_xcmplx_0),
    []).

fof(commutativity_k4_midsp_1,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)) )
     => k4_midsp_1(A,B,C) = k4_midsp_1(A,C,B) ) ),
    file(midsp_1,k4_midsp_1),
    []).

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,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,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,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)) ) ) ) ) ) ) ) ) ),
    file(midsp_3,d11_midsp_3),
    []).

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,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,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,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)) ) ) ) ) ) ) ) ) ),
    file(midsp_3,d12_midsp_3),
    []).

fof(d1_midsp_1,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))
             => k1_midsp_1(A,B,C) = k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),u1_midsp_1(A),B,C) ) ) ) ),
    file(midsp_1,d1_midsp_1),
    []).

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,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,1),u1_struct_0(B)))
                 => k4_midsp_3(A,B,C,D) = k1_funct_1(u1_midsp_3(k1_nat_1(A,2),B),k3_midsp_3(A,B,1,k1_nat_1(A,1),k2_midsp_3(A,B,C),D)) ) ) ) ) ),
    file(midsp_3,d2_midsp_3),
    []).

fof(d4_midsp_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_midsp_1(A) )
     => ( v2_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))
                       => ( k1_midsp_1(A,B,B) = B
                          & k1_midsp_1(A,B,C) = k1_midsp_1(A,C,B)
                          & k1_midsp_1(A,k1_midsp_1(A,B,C),k1_midsp_1(A,D,E)) = k1_midsp_1(A,k1_midsp_1(A,B,D),k1_midsp_1(A,C,E))
                          & ? [F] : 
                              ( m1_subset_1(F,u1_struct_0(A))
                              & k1_midsp_1(A,F,B) = C ) ) ) ) ) ) ) ) ),
    file(midsp_1,d4_midsp_1),
    []).

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,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,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))) ) ) ) ) ) ) ) ) ) ),
    file(midsp_3,d8_midsp_3),
    []).

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)) ) ),
    file(midsp_2,k10_midsp_2),
    []).

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))) ) ),
    file(midsp_2,k11_midsp_2),
    []).

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,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))) ) ),
    file(midsp_3,k11_midsp_3),
    []).

fof(dt_k1_binop_1,axiom,(
    $true ),
    file(binop_1,k1_binop_1),
    []).

fof(dt_k1_funct_1,axiom,(
    $true ),
    file(funct_1,k1_funct_1),
    []).

fof(dt_k1_midsp_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & l1_midsp_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k1_midsp_1(A,B,C),u1_struct_0(A)) ) ),
    file(midsp_1,k1_midsp_1),
    []).

fof(dt_k1_nat_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers) )
     => m2_subset_1(k1_nat_1(A,B),k1_numbers,k5_numbers) ) ),
    file(nat_1,k1_nat_1),
    []).

fof(dt_k1_numbers,axiom,(
    $true ),
    file(numbers,k1_numbers),
    []).

fof(dt_k1_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_xboole_0),
    []).

fof(dt_k1_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k1_zfmisc_1),
    []).

fof(dt_k2_binop_1,axiom,(
    ! [A,B,C,D,E,F] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(D)
        & v1_funct_2(D,k2_zfmisc_1(A,B),C)
        & m1_relset_1(D,k2_zfmisc_1(A,B),C)
        & m1_subset_1(E,A)
        & m1_subset_1(F,B) )
     => m1_subset_1(k2_binop_1(A,B,C,D,E,F),C) ) ),
    file(binop_1,k2_binop_1),
    []).

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,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(1,u1_struct_0(B))) ) ),
    file(midsp_3,k2_midsp_3),
    []).

fof(dt_k2_rlvect_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k2_rlvect_1(A,B,C),u1_struct_0(A)) ) ),
    file(rlvect_1,k2_rlvect_1),
    []).

fof(dt_k2_xcmplx_0,axiom,(
    $true ),
    file(xcmplx_0,k2_xcmplx_0),
    []).

fof(dt_k2_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k2_zfmisc_1),
    []).

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,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))) ) ),
    file(midsp_3,k3_midsp_3),
    []).

fof(dt_k4_finseq_2,axiom,(
    ! [A,B] : 
      ( v4_ordinal2(A)
     => m1_finseq_2(k4_finseq_2(A,B),B) ) ),
    file(finseq_2,k4_finseq_2),
    []).

fof(dt_k4_midsp_1,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_1(A,B,C),u1_struct_0(A)) ) ),
    file(midsp_1,k4_midsp_1),
    []).

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,2))
        & m1_subset_1(C,u1_struct_0(B))
        & m1_subset_1(D,k4_finseq_2(k1_nat_1(A,1),u1_struct_0(B))) )
     => m1_subset_1(k4_midsp_3(A,B,C,D),u1_struct_0(B)) ) ),
    file(midsp_3,k4_midsp_3),
    []).

fof(dt_k5_finseq_1,axiom,(
    $true ),
    file(finseq_1,k5_finseq_1),
    []).

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,2))
        & m1_subset_1(D,u1_struct_0(C))
        & m1_subset_1(E,k4_finseq_2(k1_nat_1(A,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,1),u1_struct_0(C))) ) ),
    file(midsp_3,k5_midsp_3),
    []).

fof(dt_k5_numbers,axiom,(
    m1_subset_1(k5_numbers,k1_zfmisc_1(k1_numbers)) ),
    file(numbers,k5_numbers),
    []).

fof(dt_k5_ordinal2,axiom,(
    $true ),
    file(ordinal2,k5_ordinal2),
    []).

fof(dt_k5_rlvect_1,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => m1_subset_1(k5_rlvect_1(A,B),u1_struct_0(A)) ) ),
    file(rlvect_1,k5_rlvect_1),
    []).

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,1),B))
        & m1_midsp_3(D,A) )
     => m1_subset_1(k6_midsp_3(A,B,C,D),B) ) ),
    file(midsp_3,k6_midsp_3),
    []).

fof(dt_k7_finseq_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => ( v1_relat_1(k7_finseq_1(A,B))
        & v1_funct_1(k7_finseq_1(A,B))
        & v1_finseq_1(k7_finseq_1(A,B)) ) ) ),
    file(finseq_1,k7_finseq_1),
    []).

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,2))
        & v3_midsp_2(C,B)
        & l1_midsp_2(C,B)
        & m1_subset_1(D,k4_finseq_2(k1_nat_1(A,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,1),u1_struct_0(u1_midsp_2(B,C)))) ) ),
    file(midsp_3,k7_midsp_3),
    []).

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,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,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,1),u1_struct_0(B))) ) ),
    file(midsp_3,k8_midsp_3),
    []).

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))) ) ),
    file(midsp_2,k9_midsp_2),
    []).

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,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,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,1),u1_struct_0(u1_midsp_2(B,C)))) ) ),
    file(midsp_3,k9_midsp_3),
    []).

fof(dt_l1_midsp_1,axiom,(
    ! [A] : 
      ( l1_midsp_1(A)
     => l1_struct_0(A) ) ),
    file(midsp_1,l1_midsp_1),
    []).

fof(dt_l1_midsp_2,axiom,(
    $true ),
    file(midsp_2,l1_midsp_2),
    []).

fof(dt_l1_midsp_3,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ! [B] : 
          ( l1_midsp_3(B,A)
         => l1_midsp_1(B) ) ) ),
    file(midsp_3,l1_midsp_3),
    []).

fof(dt_l1_rlvect_1,axiom,(
    ! [A] : 
      ( l1_rlvect_1(A)
     => l2_struct_0(A) ) ),
    file(rlvect_1,l1_rlvect_1),
    []).

fof(dt_l1_struct_0,axiom,(
    $true ),
    file(struct_0,l1_struct_0),
    []).

fof(dt_l2_struct_0,axiom,(
    ! [A] : 
      ( l2_struct_0(A)
     => l1_struct_0(A) ) ),
    file(struct_0,l2_struct_0),
    []).

fof(dt_m1_finseq_1,axiom,(
    ! [A,B] : 
      ( m1_finseq_1(B,A)
     => ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) ) ) ),
    file(finseq_1,m1_finseq_1),
    []).

fof(dt_m1_finseq_2,axiom,(
    $true ),
    file(finseq_2,m1_finseq_2),
    []).

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) ) ) ),
    file(midsp_3,m1_midsp_3),
    []).

fof(dt_m1_relset_1,axiom,(
    $true ),
    file(relset_1,m1_relset_1),
    []).

fof(dt_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    []).

fof(dt_m2_finseq_1,axiom,(
    ! [A,B] : 
      ( m2_finseq_1(B,A)
     => ( v1_funct_1(B)
        & v1_finseq_1(B)
        & m2_relset_1(B,k5_numbers,A) ) ) ),
    file(finseq_1,m2_finseq_1),
    []).

fof(dt_m2_finseq_2,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(B)
        & m1_finseq_2(B,A) )
     => ! [C] : 
          ( m2_finseq_2(C,A,B)
         => m2_finseq_1(C,A) ) ) ),
    file(finseq_2,m2_finseq_2),
    []).

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,2)) ) ) ) ),
    file(midsp_3,m2_midsp_3),
    []).

fof(dt_m2_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ),
    file(relset_1,m2_relset_1),
    []).

fof(dt_m2_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ! [C] : 
          ( m2_subset_1(C,A,B)
         => m1_subset_1(C,A) ) ) ),
    file(subset_1,m2_subset_1),
    []).

fof(dt_u1_midsp_1,axiom,(
    ! [A] : 
      ( l1_midsp_1(A)
     => ( v1_funct_1(u1_midsp_1(A))
        & v1_funct_2(u1_midsp_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
        & m2_relset_1(u1_midsp_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) ) ) ),
    file(midsp_1,u1_midsp_1),
    []).

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)) ) ) ),
    file(midsp_2,u1_midsp_2),
    []).

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)) ) ) ),
    file(midsp_3,u1_midsp_3),
    []).

fof(dt_u1_struct_0,axiom,(
    $true ),
    file(struct_0,u1_struct_0),
    []).

fof(existence_l1_midsp_1,axiom,(
    ? [A] : l1_midsp_1(A) ),
    file(midsp_1,l1_midsp_1),
    []).

fof(existence_l1_midsp_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_midsp_1(A) )
     => ? [B] : l1_midsp_2(B,A) ) ),
    file(midsp_2,l1_midsp_2),
    []).

fof(existence_l1_midsp_3,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ? [B] : l1_midsp_3(B,A) ) ),
    file(midsp_3,l1_midsp_3),
    []).

fof(existence_l1_rlvect_1,axiom,(
    ? [A] : l1_rlvect_1(A) ),
    file(rlvect_1,l1_rlvect_1),
    []).

fof(existence_l1_struct_0,axiom,(
    ? [A] : l1_struct_0(A) ),
    file(struct_0,l1_struct_0),
    []).

fof(existence_l2_struct_0,axiom,(
    ? [A] : l2_struct_0(A) ),
    file(struct_0,l2_struct_0),
    []).

fof(existence_m1_finseq_1,axiom,(
    ! [A] : 
    ? [B] : m1_finseq_1(B,A) ),
    file(finseq_1,m1_finseq_1),
    []).

fof(existence_m1_finseq_2,axiom,(
    ! [A] : 
    ? [B] : m1_finseq_2(B,A) ),
    file(finseq_2,m1_finseq_2),
    []).

fof(existence_m1_midsp_3,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ? [B] : m1_midsp_3(B,A) ) ),
    file(midsp_3,m1_midsp_3),
    []).

fof(existence_m1_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m1_relset_1(C,A,B) ),
    file(relset_1,m1_relset_1),
    []).

fof(existence_m1_subset_1,axiom,(
    ! [A] : 
    ? [B] : m1_subset_1(B,A) ),
    file(subset_1,m1_subset_1),
    []).

fof(existence_m2_finseq_1,axiom,(
    ! [A] : 
    ? [B] : m2_finseq_1(B,A) ),
    file(finseq_1,m2_finseq_1),
    []).

fof(existence_m2_finseq_2,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(B)
        & m1_finseq_2(B,A) )
     => ? [C] : m2_finseq_2(C,A,B) ) ),
    file(finseq_2,m2_finseq_2),
    []).

fof(existence_m2_midsp_3,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ? [B] : m2_midsp_3(B,A) ) ),
    file(midsp_3,m2_midsp_3),
    []).

fof(existence_m2_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m2_relset_1(C,A,B) ),
    file(relset_1,m2_relset_1),
    []).

fof(existence_m2_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ? [C] : m2_subset_1(C,A,B) ) ),
    file(subset_1,m2_subset_1),
    []).

fof(fc1_finseq_2,axiom,(
    ! [A,B] : 
      ( ( v4_ordinal2(A)
        & ~ v1_xboole_0(B) )
     => ~ v1_xboole_0(k4_finseq_2(A,B)) ) ),
    file(finseq_2,fc1_finseq_2),
    []).

fof(fc1_nat_1,axiom,(
    ! [A,B] : 
      ( ( v4_ordinal2(A)
        & v4_ordinal2(B) )
     => ( v4_ordinal2(k2_xcmplx_0(A,B))
        & v1_xcmplx_0(k2_xcmplx_0(A,B))
        & v1_xreal_0(k2_xcmplx_0(A,B)) ) ) ),
    file(nat_1,fc1_nat_1),
    []).

fof(fc1_struct_0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ~ v1_xboole_0(u1_struct_0(A)) ) ),
    file(struct_0,fc1_struct_0),
    []).

fof(fc3_nat_1,axiom,(
    ! [A,B] : 
      ( ( v4_ordinal2(A)
        & ~ v1_xboole_0(B)
        & v4_ordinal2(B) )
     => ( ~ v1_xboole_0(k2_xcmplx_0(A,B))
        & v4_ordinal2(k2_xcmplx_0(A,B))
        & v1_xcmplx_0(k2_xcmplx_0(A,B))
        & v1_xreal_0(k2_xcmplx_0(A,B)) ) ) ),
    file(nat_1,fc3_nat_1),
    []).

fof(fc4_nat_1,axiom,(
    ! [A,B] : 
      ( ( v4_ordinal2(A)
        & ~ v1_xboole_0(B)
        & v4_ordinal2(B) )
     => ( ~ v1_xboole_0(k2_xcmplx_0(B,A))
        & v4_ordinal2(k2_xcmplx_0(B,A))
        & v1_xcmplx_0(k2_xcmplx_0(B,A))
        & v1_xreal_0(k2_xcmplx_0(B,A)) ) ) ),
    file(nat_1,fc4_nat_1),
    []).

fof(l42_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] : 
                  ( m2_finseq_2(D,u1_struct_0(B),k4_finseq_2(k1_nat_1(A,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,1),u1_struct_0(u1_midsp_2(B,E))))
                         => ( k9_midsp_3(A,B,E,C,D) = F
                           => k11_midsp_3(A,B,E,F) = k9_midsp_2(B,E,C,k4_midsp_3(A,B,C,D)) ) ) ) ) ) ) ) ),
    file(midsp_3,l42_midsp_3),
    []).

fof(l43_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] : 
                  ( m2_finseq_2(D,u1_struct_0(B),k4_finseq_2(k1_nat_1(A,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,1),u1_struct_0(u1_midsp_2(B,E))))
                         => ( k8_midsp_3(A,B,E,C,F) = D
                           => k11_midsp_3(A,B,E,F) = k9_midsp_2(B,E,C,k4_midsp_3(A,B,C,D)) ) ) ) ) ) ) ) ),
    file(midsp_3,l43_midsp_3),
    []).

fof(l51_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] : 
                        ( m1_subset_1(E,u1_struct_0(C))
                       => ! [F] : 
                            ( m1_subset_1(F,u1_struct_0(C))
                           => ! [G] : 
                                ( m1_subset_1(G,u1_struct_0(C))
                               => ! [H] : 
                                    ( m2_finseq_2(H,u1_struct_0(C),k4_finseq_2(k1_nat_1(A,1),u1_struct_0(C)))
                                   => ( k4_midsp_1(C,E,G) = k4_midsp_1(C,k6_midsp_3(A,u1_struct_0(C),H,B),F)
                                     => ( k4_midsp_3(A,C,E,k5_midsp_3(A,B,C,k4_midsp_1(C,k6_midsp_3(A,u1_struct_0(C),H,B),F),H)) = k4_midsp_1(C,k4_midsp_3(A,C,E,H),k4_midsp_3(A,C,E,k5_midsp_3(A,B,C,F,H)))
                                      <=> k9_midsp_2(C,D,E,k4_midsp_3(A,C,E,k5_midsp_3(A,B,C,G,H))) = k2_rlvect_1(u1_midsp_2(C,D),k9_midsp_2(C,D,E,k4_midsp_3(A,C,E,H)),k9_midsp_2(C,D,E,k4_midsp_3(A,C,E,k5_midsp_3(A,B,C,F,H)))) ) ) ) ) ) ) ) ) ) ) ) ),
    file(midsp_3,l51_midsp_3),
    []).

fof(l52_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) )
                 => ( ! [E] : 
                        ( m2_finseq_2(E,u1_struct_0(u1_midsp_2(C,D)),k4_finseq_2(k1_nat_1(A,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))) ) )
                   => r2_midsp_3(A,B,C) ) ) ) ) ) ),
    file(midsp_3,l52_midsp_3),
    []).

fof(rc1_finseq_2,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_finseq_2(B,A)
      & ~ v1_xboole_0(B) ) ),
    file(finseq_2,rc1_finseq_2),
    []).

fof(rc1_nat_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v4_ordinal2(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A) ) ),
    file(nat_1,rc1_nat_1),
    []).

fof(rc2_midsp_3,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ? [B] : 
          ( l1_midsp_3(B,A)
          & ~ v3_struct_0(B) ) ) ),
    file(midsp_3,rc2_midsp_3),
    []).

fof(rc2_nat_1,axiom,(
    ? [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
      & ~ v1_xboole_0(A)
      & v3_ordinal1(A) ) ),
    file(nat_1,rc2_nat_1),
    []).

fof(rc3_midsp_3,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ? [B] : 
          ( l1_midsp_3(B,k1_nat_1(A,2))
          & ~ v3_struct_0(B)
          & v2_midsp_1(B) ) ) ),
    file(midsp_3,rc3_midsp_3),
    []).

fof(rc3_nat_1,axiom,(
    ? [A] : 
      ( m1_subset_1(A,k5_numbers)
      & ~ v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A)
      & v4_ordinal2(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A) ) ),
    file(nat_1,rc3_nat_1),
    []).

fof(rc3_struct_0,axiom,(
    ? [A] : 
      ( l1_struct_0(A)
      & ~ v3_struct_0(A) ) ),
    file(struct_0,rc3_struct_0),
    []).

fof(rc4_struct_0,axiom,(
    ? [A] : 
      ( l2_struct_0(A)
      & ~ v3_struct_0(A) ) ),
    file(struct_0,rc4_struct_0),
    []).

fof(rc5_struct_0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & ~ v1_xboole_0(B) ) ) ),
    file(struct_0,rc5_struct_0),
    []).

fof(redefinition_k1_nat_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers) )
     => k1_nat_1(A,B) = k2_xcmplx_0(A,B) ) ),
    file(nat_1,k1_nat_1),
    []).

fof(redefinition_k2_binop_1,axiom,(
    ! [A,B,C,D,E,F] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(D)
        & v1_funct_2(D,k2_zfmisc_1(A,B),C)
        & m1_relset_1(D,k2_zfmisc_1(A,B),C)
        & m1_subset_1(E,A)
        & m1_subset_1(F,B) )
     => k2_binop_1(A,B,C,D,E,F) = k1_binop_1(D,E,F) ) ),
    file(binop_1,k2_binop_1),
    []).

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,2))
        & m1_subset_1(C,u1_struct_0(B)) )
     => k2_midsp_3(A,B,C) = k5_finseq_1(C) ) ),
    file(midsp_3,k2_midsp_3),
    []).

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,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) ) ),
    file(midsp_3,k3_midsp_3),
    []).

fof(redefinition_k4_midsp_1,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)) )
     => k4_midsp_1(A,B,C) = k1_midsp_1(A,B,C) ) ),
    file(midsp_1,k4_midsp_1),
    []).

fof(redefinition_k5_numbers,axiom,(
    k5_numbers = k5_ordinal2 ),
    file(numbers,k5_numbers),
    []).

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,1),B))
        & m1_midsp_3(D,A) )
     => k6_midsp_3(A,B,C,D) = k1_funct_1(C,D) ) ),
    file(midsp_3,k6_midsp_3),
    []).

fof(redefinition_m2_finseq_1,axiom,(
    ! [A,B] : 
      ( m2_finseq_1(B,A)
    <=> m1_finseq_1(B,A) ) ),
    file(finseq_1,m2_finseq_1),
    []).

fof(redefinition_m2_finseq_2,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(B)
        & m1_finseq_2(B,A) )
     => ! [C] : 
          ( m2_finseq_2(C,A,B)
        <=> m1_subset_1(C,B) ) ) ),
    file(finseq_2,m2_finseq_2),
    []).

fof(redefinition_m2_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
    <=> m1_relset_1(C,A,B) ) ),
    file(relset_1,m2_relset_1),
    []).

fof(redefinition_m2_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ! [C] : 
          ( m2_subset_1(C,A,B)
        <=> m1_subset_1(C,B) ) ) ),
    file(subset_1,m2_subset_1),
    []).

fof(reflexivity_r1_tarski,axiom,(
    ! [A,B] : r1_tarski(A,A) ),
    file(tarski,r1_tarski),
    []).

fof(spc1_boole,axiom,(
    ~ v1_xboole_0(1) ),
    file(boole,spc1_boole),
    []).

fof(spc1_numerals,axiom,
    ( v2_xreal_0(1)
    & m1_subset_1(1,k5_numbers) ),
    file(numerals,spc1_numerals),
    []).

fof(spc2_boole,axiom,(
    ~ v1_xboole_0(2) ),
    file(boole,spc2_boole),
    []).

fof(spc2_numerals,axiom,
    ( v2_xreal_0(2)
    & m1_subset_1(2,k5_numbers) ),
    file(numerals,spc2_numerals),
    []).

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,2)) )
         => ! [C] : 
              ( m2_finseq_2(C,u1_struct_0(B),k4_finseq_2(k1_nat_1(A,1),u1_struct_0(B)))
             => ! [D] : 
                  ( m2_finseq_2(D,u1_struct_0(B),k4_finseq_2(k1_nat_1(A,1),u1_struct_0(B)))
                 => ( ! [E] : 
                        ( m1_midsp_3(E,A)
                       => k1_funct_1(C,E) = k1_funct_1(D,E) )
                   => C = D ) ) ) ) ) ),
    file(midsp_3,t11_midsp_3),
    []).

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,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,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) ) ) ) ) ) ) ) ) ) ),
    file(midsp_3,t12_midsp_3),
    []).

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,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,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) ) ) ) ) ) ) ) ) ) ) ),
    file(midsp_3,t15_midsp_3),
    []).

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,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,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,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 ) ) ) ) ) ) ) ),
    file(midsp_3,t17_midsp_3),
    []).

fof(t1_subset,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => m1_subset_1(A,B) ) ),
    file(subset,t1_subset),
    []).

fof(t2_subset,axiom,(
    ! [A,B] : 
      ( m1_subset_1(A,B)
     => ( v1_xboole_0(B)
        | r2_hidden(A,B) ) ) ),
    file(subset,t2_subset),
    []).

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) ) ) ) ) ),
    file(midsp_3,t32_midsp_3),
    []).

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)) ) ) ) ) ) ) ) ),
    file(midsp_2,t36_midsp_2),
    []).

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 ) ) ) ) ) ) ) ) ) ),
    file(midsp_2,t39_midsp_2),
    []).

fof(t3_subset,axiom,(
    ! [A,B] : 
      ( m1_subset_1(A,k1_zfmisc_1(B))
    <=> r1_tarski(A,B) ) ),
    file(subset,t3_subset),
    []).

fof(t4_subset,axiom,(
    ! [A,B,C] : 
      ( ( r2_hidden(A,B)
        & m1_subset_1(B,k1_zfmisc_1(C)) )
     => m1_subset_1(A,C) ) ),
    file(subset,t4_subset),
    []).

fof(t5_subset,axiom,(
    ! [A,B,C] : ~ ( r2_hidden(A,B)
      & m1_subset_1(B,k1_zfmisc_1(C))
      & v1_xboole_0(C) ) ),
    file(subset,t5_subset),
    []).

fof(t6_boole,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => A = k1_xboole_0 ) ),
    file(boole,t6_boole),
    []).

fof(t7_boole,axiom,(
    ! [A,B] : ~ ( r2_hidden(A,B)
      & v1_xboole_0(B) ) ),
    file(boole,t7_boole),
    []).

fof(t8_boole,axiom,(
    ! [A,B] : ~ ( v1_xboole_0(A)
      & A != B
      & v1_xboole_0(B) ) ),
    file(boole,t8_boole),
    []).