% Mizar problem: t7_measure4,measure4,319,50 
fof(t7_measure4,conjecture,(
    ! [A,B] : 
      ( m1_subset_1(B,k3_supinf_1)
     => ! [C] : 
          ( m1_subset_1(C,k3_supinf_1)
         => ? [D] : 
              ( v1_funct_1(D)
              & v1_funct_2(D,k1_zfmisc_1(A),k3_supinf_1)
              & m2_relset_1(D,k1_zfmisc_1(A),k3_supinf_1)
              & ! [E] : 
                  ( m1_subset_1(E,k1_zfmisc_1(A))
                 => ( ( E = k1_xboole_0
                     => k1_measure1(k1_zfmisc_1(A),D,E) = B )
                    & ( E != k1_xboole_0
                     => k1_measure1(k1_zfmisc_1(A),D,E) = C ) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_funct_1,cc1_relset_1,cc1_supinf_1,cc2_funct_1,dt_k1_funct_1,dt_k1_measure1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k3_supinf_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,fc1_subset_1,fc1_supinf_1,fc1_xboole_0,fc4_subset_1,rc1_funct_1,rc1_subset_1,rc1_xboole_0,rc2_funct_1,rc2_subset_1,rc2_xboole_0,rc3_funct_1,rc3_supinf_1,redefinition_k1_measure1,redefinition_m2_relset_1,reflexivity_r1_tarski,s1_funct_2__e2_8__measure4,t1_subset,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole]),
    [file(measure4,t7_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_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(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_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_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k2_zfmisc_1),
    []).

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

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(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(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_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_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_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_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_tarski,axiom,(
    ! [A,B] : r1_tarski(A,A) ),
    file(tarski,r1_tarski),
    []).

fof(s1_funct_2__e2_8__measure4,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k3_supinf_1)
        & m1_subset_1(C,k3_supinf_1) )
     => ( ! [D] : ~ ( r2_hidden(D,k1_zfmisc_1(A))
            & ! [E] : ~ ( r2_hidden(E,k3_supinf_1)
                & ( D = k1_xboole_0
                 => E = B )
                & ( D != k1_xboole_0
                 => E = C ) ) )
       => ? [D] : 
            ( v1_funct_1(D)
            & v1_funct_2(D,k1_zfmisc_1(A),k3_supinf_1)
            & m2_relset_1(D,k1_zfmisc_1(A),k3_supinf_1)
            & ! [E] : 
                ( r2_hidden(E,k1_zfmisc_1(A))
               => ( ( E = k1_xboole_0
                   => k1_funct_1(D,E) = B )
                  & ( E != k1_xboole_0
                   => k1_funct_1(D,E) = C ) ) ) ) ) ) ),
    file(measure4,s1_funct_2__e2_8__measure4),
    []).

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(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),
    []).