% Mizar problem: t25_measure4,measure4,1120,43 
fof(t25_measure4,conjecture,(
    ! [A,B] : 
      ( m1_measure4(B,A)
     => r1_measure3(A,k3_measure4(A,B),k7_measure4(A,B)) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_funct_1,cc1_measure1,cc1_nat_1,cc1_relset_1,cc1_supinf_1,cc2_funct_1,cc2_measure1,cc2_nat_1,cc2_supinf_1,cc3_measure1,cc3_nat_1,cc4_measure1,connectedness_r1_supinf_1,d2_measure3,d2_measure4,d4_measure1,d4_measure4,dt_k19_supinf_2,dt_k1_funct_1,dt_k1_measure1,dt_k1_measure4,dt_k1_numbers,dt_k1_supinf_2,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_measure4,dt_k2_relat_1,dt_k2_zfmisc_1,dt_k3_measure4,dt_k3_supinf_1,dt_k3_tarski,dt_k5_measure4,dt_k5_numbers,dt_k5_ordinal2,dt_k5_relat_1,dt_k5_setfam_1,dt_k7_measure4,dt_m1_measure4,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_m3_measure1,existence_m1_measure4,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,existence_m3_measure1,fc1_funct_1,fc1_measure4,fc1_numbers,fc1_ordinal2,fc1_subset_1,fc1_supinf_1,fc1_xboole_0,fc4_subset_1,rc1_funct_1,rc1_measure1,rc1_nat_1,rc1_subset_1,rc1_xboole_0,rc2_funct_1,rc2_nat_1,rc2_subset_1,rc2_xboole_0,rc3_funct_1,rc3_measure1,rc3_nat_1,rc3_supinf_1,redefinition_k1_measure1,redefinition_k1_measure4,redefinition_k2_measure4,redefinition_k5_numbers,redefinition_k5_setfam_1,redefinition_k7_measure4,redefinition_m2_relset_1,reflexivity_r1_supinf_1,reflexivity_r1_tarski,t1_subset,t22_supinf_1,t24_measure4,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole]),
    [file(measure4,t25_measure4)]).

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

fof(cc1_funct_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_funct_1(A) ) ),
    file(funct_1,cc1_funct_1),
    []).

fof(cc1_measure1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ( ( v1_finsub_1(B)
          & v1_prob_1(B,A) )
       => v2_finsub_1(B) ) ) ),
    file(measure1,cc1_measure1),
    []).

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(cc1_supinf_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k3_supinf_1)
     => v3_supinf_1(A) ) ),
    file(supinf_1,cc1_supinf_1),
    []).

fof(cc2_funct_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_xboole_0(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v2_funct_1(A) ) ) ),
    file(funct_1,cc2_funct_1),
    []).

fof(cc2_measure1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ( ( v2_finsub_1(B)
          & v1_prob_1(B,A) )
       => v1_finsub_1(B) ) ) ),
    file(measure1,cc2_measure1),
    []).

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(cc2_supinf_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_numbers)
     => ( v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & v3_supinf_1(A) ) ) ),
    file(supinf_1,cc2_supinf_1),
    []).

fof(cc3_measure1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ( ( ~ v1_xboole_0(B)
          & v1_prob_1(B,A)
          & v1_measure1(B,A) )
       => ( ~ v1_xboole_0(B)
          & v1_prob_1(B,A)
          & v1_measure1(B,A) ) ) ) ),
    file(measure1,cc3_measure1),
    []).

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(cc4_measure1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ( ( ~ v1_xboole_0(B)
          & v1_prob_1(B,A)
          & v1_measure1(B,A) )
       => ( ~ v1_xboole_0(B)
          & v1_finsub_1(B) ) ) ) ),
    file(measure1,cc4_measure1),
    []).

fof(connectedness_r1_supinf_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k3_supinf_1)
        & m1_subset_1(B,k3_supinf_1) )
     => ( r1_supinf_1(A,B)
        | r1_supinf_1(B,A) ) ) ),
    file(supinf_1,r1_supinf_1),
    []).

fof(d2_measure3,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(B)
        & v1_prob_1(B,A)
        & v1_measure1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
     => ! [C] : 
          ( m3_measure1(C,A,B)
         => ( r1_measure3(A,B,C)
          <=> ! [D] : 
                ( m1_subset_1(D,k1_zfmisc_1(A))
               => ! [E] : 
                    ( ( r2_hidden(E,B)
                      & r1_tarski(D,E)
                      & k1_funct_1(C,E) = k1_supinf_2 )
                   => r2_hidden(D,B) ) ) ) ) ) ),
    file(measure3,d2_measure3),
    []).

fof(d2_measure4,axiom,(
    ! [A,B] : 
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k1_zfmisc_1(A),k3_supinf_1)
        & m2_relset_1(B,k1_zfmisc_1(A),k3_supinf_1) )
     => ( m1_measure4(B,A)
      <=> ( v6_supinf_2(B,k1_zfmisc_1(A))
          & k1_funct_1(B,k1_xboole_0) = k1_supinf_2
          & ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(A))
             => ! [D] : 
                  ( m1_subset_1(D,k1_zfmisc_1(A))
                 => ( r1_tarski(C,D)
                   => ( r1_supinf_1(k1_measure1(k1_zfmisc_1(A),B,C),k1_measure1(k1_zfmisc_1(A),B,D))
                      & ! [E] : 
                          ( ( v1_funct_1(E)
                            & v1_funct_2(E,k5_numbers,k1_zfmisc_1(A))
                            & m2_relset_1(E,k5_numbers,k1_zfmisc_1(A)) )
                         => r1_supinf_1(k1_measure1(k1_zfmisc_1(A),B,k5_setfam_1(A,k1_measure4(A,E))),k19_supinf_2(k2_measure4(k5_numbers,k1_zfmisc_1(A),k3_supinf_1,E,B))) ) ) ) ) ) ) ) ) ),
    file(measure4,d2_measure4),
    []).

fof(d4_measure1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,A,k3_supinf_1)
            & m2_relset_1(B,A,k3_supinf_1) )
         => ( v6_supinf_2(B,A)
          <=> ! [C] : 
                ( m1_subset_1(C,A)
               => r1_supinf_1(k1_supinf_2,k1_measure1(A,B,C)) ) ) ) ) ),
    file(measure1,d4_measure1),
    []).

fof(d4_measure4,axiom,(
    ! [A,B] : 
      ( m1_measure4(B,A)
     => ! [C] : 
          ( ( v1_funct_1(C)
            & v1_funct_2(C,k3_measure4(A,B),k3_supinf_1)
            & m2_relset_1(C,k3_measure4(A,B),k3_supinf_1) )
         => ( C = k5_measure4(A,B)
          <=> ! [D] : 
                ( m1_subset_1(D,k1_zfmisc_1(A))
               => ( r2_hidden(D,k3_measure4(A,B))
                 => k1_funct_1(C,D) = k1_measure1(k1_zfmisc_1(A),B,D) ) ) ) ) ) ),
    file(measure4,d4_measure4),
    []).

fof(dt_k19_supinf_2,axiom,(
    ! [A] : 
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k3_supinf_1)
        & m1_relset_1(A,k5_numbers,k3_supinf_1) )
     => m1_subset_1(k19_supinf_2(A),k3_supinf_1) ) ),
    file(supinf_2,k19_supinf_2),
    []).

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

fof(dt_k1_measure1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(B)
        & v1_funct_2(B,A,k3_supinf_1)
        & m1_relset_1(B,A,k3_supinf_1)
        & m1_subset_1(C,A) )
     => m1_subset_1(k1_measure1(A,B,C),k3_supinf_1) ) ),
    file(measure1,k1_measure1),
    []).

fof(dt_k1_measure4,axiom,(
    ! [A,B] : 
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
        & m1_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
     => m1_subset_1(k1_measure4(A,B),k1_zfmisc_1(k1_zfmisc_1(A))) ) ),
    file(measure4,k1_measure4),
    []).

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

fof(dt_k1_supinf_2,axiom,(
    m1_subset_1(k1_supinf_2,k3_supinf_1) ),
    file(supinf_2,k1_supinf_2),
    []).

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_measure4,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m1_relset_1(D,A,B)
        & v1_funct_1(E)
        & v1_funct_2(E,B,C)
        & m1_relset_1(E,B,C) )
     => ( v1_funct_1(k2_measure4(A,B,C,D,E))
        & v1_funct_2(k2_measure4(A,B,C,D,E),A,C)
        & m2_relset_1(k2_measure4(A,B,C,D,E),A,C) ) ) ),
    file(measure4,k2_measure4),
    []).

fof(dt_k2_relat_1,axiom,(
    $true ),
    file(relat_1,k2_relat_1),
    []).

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

fof(dt_k3_measure4,axiom,(
    ! [A,B] : 
      ( m1_measure4(B,A)
     => ( ~ v1_xboole_0(k3_measure4(A,B))
        & m1_subset_1(k3_measure4(A,B),k1_zfmisc_1(k1_zfmisc_1(A))) ) ) ),
    file(measure4,k3_measure4),
    []).

fof(dt_k3_supinf_1,axiom,(
    $true ),
    file(supinf_1,k3_supinf_1),
    []).

fof(dt_k3_tarski,axiom,(
    $true ),
    file(tarski,k3_tarski),
    []).

fof(dt_k5_measure4,axiom,(
    ! [A,B] : 
      ( m1_measure4(B,A)
     => ( v1_funct_1(k5_measure4(A,B))
        & v1_funct_2(k5_measure4(A,B),k3_measure4(A,B),k3_supinf_1)
        & m2_relset_1(k5_measure4(A,B),k3_measure4(A,B),k3_supinf_1) ) ) ),
    file(measure4,k5_measure4),
    []).

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_relat_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_relat_1(B) )
     => v1_relat_1(k5_relat_1(A,B)) ) ),
    file(relat_1,k5_relat_1),
    []).

fof(dt_k5_setfam_1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => m1_subset_1(k5_setfam_1(A,B),k1_zfmisc_1(A)) ) ),
    file(setfam_1,k5_setfam_1),
    []).

fof(dt_k7_measure4,axiom,(
    ! [A,B] : 
      ( m1_measure4(B,A)
     => m3_measure1(k7_measure4(A,B),A,k3_measure4(A,B)) ) ),
    file(measure4,k7_measure4),
    []).

fof(dt_m1_measure4,axiom,(
    ! [A,B] : 
      ( m1_measure4(B,A)
     => ( v1_funct_1(B)
        & v1_funct_2(B,k1_zfmisc_1(A),k3_supinf_1)
        & m2_relset_1(B,k1_zfmisc_1(A),k3_supinf_1) ) ) ),
    file(measure4,m1_measure4),
    []).

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_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_m3_measure1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(B)
        & v1_prob_1(B,A)
        & v1_measure1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
     => ! [C] : 
          ( m3_measure1(C,A,B)
         => ( v1_funct_1(C)
            & v1_funct_2(C,B,k3_supinf_1)
            & m2_relset_1(C,B,k3_supinf_1) ) ) ) ),
    file(measure1,m3_measure1),
    []).

fof(existence_m1_measure4,axiom,(
    ! [A] : 
    ? [B] : m1_measure4(B,A) ),
    file(measure4,m1_measure4),
    []).

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_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m2_relset_1(C,A,B) ),
    file(relset_1,m2_relset_1),
    []).

fof(existence_m3_measure1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(B)
        & v1_prob_1(B,A)
        & v1_measure1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
     => ? [C] : m3_measure1(C,A,B) ) ),
    file(measure1,m3_measure1),
    []).

fof(fc1_funct_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B) )
     => ( v1_relat_1(k5_relat_1(A,B))
        & v1_funct_1(k5_relat_1(A,B)) ) ) ),
    file(funct_1,fc1_funct_1),
    []).

fof(fc1_measure4,axiom,(
    ! [A,B] : 
      ( m1_measure4(B,A)
     => ( ~ v1_xboole_0(k3_measure4(A,B))
        & v1_prob_1(k3_measure4(A,B),A)
        & v1_finsub_1(k3_measure4(A,B))
        & v2_finsub_1(k3_measure4(A,B))
        & v1_measure1(k3_measure4(A,B),A) ) ) ),
    file(measure4,fc1_measure4),
    []).

fof(fc1_numbers,axiom,(
    ~ v1_xboole_0(k1_numbers) ),
    file(numbers,fc1_numbers),
    []).

fof(fc1_ordinal2,axiom,
    ( v1_ordinal1(k5_ordinal2)
    & v2_ordinal1(k5_ordinal2)
    & v3_ordinal1(k5_ordinal2)
    & ~ v1_xboole_0(k5_ordinal2) ),
    file(ordinal2,fc1_ordinal2),
    []).

fof(fc1_subset_1,axiom,(
    ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ),
    file(subset_1,fc1_subset_1),
    []).

fof(fc1_supinf_1,axiom,(
    ~ v1_xboole_0(k3_supinf_1) ),
    file(supinf_1,fc1_supinf_1),
    []).

fof(fc1_xboole_0,axiom,(
    v1_xboole_0(k1_xboole_0) ),
    file(xboole_0,fc1_xboole_0),
    []).

fof(fc4_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ~ v1_xboole_0(k2_zfmisc_1(A,B)) ) ),
    file(subset_1,fc4_subset_1),
    []).

fof(rc1_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc1_funct_1),
    []).

fof(rc1_measure1,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
      & ~ v1_xboole_0(B)
      & v1_finsub_1(B)
      & v2_finsub_1(B)
      & v1_prob_1(B,A) ) ),
    file(measure1,rc1_measure1),
    []).

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(rc1_subset_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B) ) ) ),
    file(subset_1,rc1_subset_1),
    []).

fof(rc1_xboole_0,axiom,(
    ? [A] : v1_xboole_0(A) ),
    file(xboole_0,rc1_xboole_0),
    []).

fof(rc2_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_xboole_0(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc2_funct_1),
    []).

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(rc2_subset_1,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
      & v1_xboole_0(B) ) ),
    file(subset_1,rc2_subset_1),
    []).

fof(rc2_xboole_0,axiom,(
    ? [A] : ~ v1_xboole_0(A) ),
    file(xboole_0,rc2_xboole_0),
    []).

fof(rc3_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A) ) ),
    file(funct_1,rc3_funct_1),
    []).

fof(rc3_measure1,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
      & ~ v1_xboole_0(B)
      & v1_prob_1(B,A)
      & v1_measure1(B,A) ) ),
    file(measure1,rc3_measure1),
    []).

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_supinf_1,axiom,(
    ? [A] : v3_supinf_1(A) ),
    file(supinf_1,rc3_supinf_1),
    []).

fof(redefinition_k1_measure1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(B)
        & v1_funct_2(B,A,k3_supinf_1)
        & m1_relset_1(B,A,k3_supinf_1)
        & m1_subset_1(C,A) )
     => k1_measure1(A,B,C) = k1_funct_1(B,C) ) ),
    file(measure1,k1_measure1),
    []).

fof(redefinition_k1_measure4,axiom,(
    ! [A,B] : 
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
        & m1_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
     => k1_measure4(A,B) = k2_relat_1(B) ) ),
    file(measure4,k1_measure4),
    []).

fof(redefinition_k2_measure4,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m1_relset_1(D,A,B)
        & v1_funct_1(E)
        & v1_funct_2(E,B,C)
        & m1_relset_1(E,B,C) )
     => k2_measure4(A,B,C,D,E) = k5_relat_1(D,E) ) ),
    file(measure4,k2_measure4),
    []).

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

fof(redefinition_k5_setfam_1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => k5_setfam_1(A,B) = k3_tarski(B) ) ),
    file(setfam_1,k5_setfam_1),
    []).

fof(redefinition_k7_measure4,axiom,(
    ! [A,B] : 
      ( m1_measure4(B,A)
     => k7_measure4(A,B) = k5_measure4(A,B) ) ),
    file(measure4,k7_measure4),
    []).

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(reflexivity_r1_supinf_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k3_supinf_1)
        & m1_subset_1(B,k3_supinf_1) )
     => r1_supinf_1(A,A) ) ),
    file(supinf_1,r1_supinf_1),
    []).

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

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

fof(t22_supinf_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k3_supinf_1)
     => ! [B] : 
          ( m1_subset_1(B,k3_supinf_1)
         => ( ( r1_supinf_1(A,B)
              & r1_supinf_1(B,A) )
           => A = B ) ) ) ),
    file(supinf_1,t22_supinf_1),
    []).

fof(t24_measure4,axiom,(
    ! [A,B] : 
      ( m1_measure4(B,A)
     => ! [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(A))
         => ( k1_measure1(k1_zfmisc_1(A),B,C) = k1_supinf_2
           => r2_hidden(C,k3_measure4(A,B)) ) ) ) ),
    file(measure4,t24_measure4),
    []).

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

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),
    []).