% Mizar ND problem: t6_bvfunc_8,bvfunc_8,405,31 
fof(dh_c1_6__bvfunc_8,definition,
    ( ( ~ v1_xboole_0(c1_6__bvfunc_8)
     => ! [A] : 
          ( m2_fraenkel(A,c1_6__bvfunc_8,k6_margrel1,k1_fraenkel(c1_6__bvfunc_8,k6_margrel1))
         => ! [B] : 
              ( m2_fraenkel(B,c1_6__bvfunc_8,k6_margrel1,k1_fraenkel(c1_6__bvfunc_8,k6_margrel1))
             => A = k8_bvfunc_1(c1_6__bvfunc_8,k6_valuat_1(c1_6__bvfunc_8,A,B),k6_valuat_1(c1_6__bvfunc_8,A,k5_valuat_1(c1_6__bvfunc_8,B))) ) ) )
   => ! [C] : 
        ( ~ v1_xboole_0(C)
       => ! [D] : 
            ( m2_fraenkel(D,C,k6_margrel1,k1_fraenkel(C,k6_margrel1))
           => ! [E] : 
                ( m2_fraenkel(E,C,k6_margrel1,k1_fraenkel(C,k6_margrel1))
               => D = k8_bvfunc_1(C,k6_valuat_1(C,D,E),k6_valuat_1(C,D,k5_valuat_1(C,E))) ) ) ) ),
    introduced(definition,[new_symbol(c1_6__bvfunc_8),file(bvfunc_8,c1_6__bvfunc_8)]),
    [interesting(0.8),axiom,file(bvfunc_8,c1_6__bvfunc_8)]).

fof(dh_c2_6__bvfunc_8,definition,
    ( ( m2_fraenkel(c2_6__bvfunc_8,c1_6__bvfunc_8,k6_margrel1,k1_fraenkel(c1_6__bvfunc_8,k6_margrel1))
     => ! [A] : 
          ( m2_fraenkel(A,c1_6__bvfunc_8,k6_margrel1,k1_fraenkel(c1_6__bvfunc_8,k6_margrel1))
         => c2_6__bvfunc_8 = k8_bvfunc_1(c1_6__bvfunc_8,k6_valuat_1(c1_6__bvfunc_8,c2_6__bvfunc_8,A),k6_valuat_1(c1_6__bvfunc_8,c2_6__bvfunc_8,k5_valuat_1(c1_6__bvfunc_8,A))) ) )
   => ! [B] : 
        ( m2_fraenkel(B,c1_6__bvfunc_8,k6_margrel1,k1_fraenkel(c1_6__bvfunc_8,k6_margrel1))
       => ! [C] : 
            ( m2_fraenkel(C,c1_6__bvfunc_8,k6_margrel1,k1_fraenkel(c1_6__bvfunc_8,k6_margrel1))
           => B = k8_bvfunc_1(c1_6__bvfunc_8,k6_valuat_1(c1_6__bvfunc_8,B,C),k6_valuat_1(c1_6__bvfunc_8,B,k5_valuat_1(c1_6__bvfunc_8,C))) ) ) ),
    introduced(definition,[new_symbol(c2_6__bvfunc_8),file(bvfunc_8,c2_6__bvfunc_8)]),
    [interesting(0.8),axiom,file(bvfunc_8,c2_6__bvfunc_8)]).

fof(dh_c3_6__bvfunc_8,definition,
    ( ( m2_fraenkel(c3_6__bvfunc_8,c1_6__bvfunc_8,k6_margrel1,k1_fraenkel(c1_6__bvfunc_8,k6_margrel1))
     => c2_6__bvfunc_8 = k8_bvfunc_1(c1_6__bvfunc_8,k6_valuat_1(c1_6__bvfunc_8,c2_6__bvfunc_8,c3_6__bvfunc_8),k6_valuat_1(c1_6__bvfunc_8,c2_6__bvfunc_8,k5_valuat_1(c1_6__bvfunc_8,c3_6__bvfunc_8))) )
   => ! [A] : 
        ( m2_fraenkel(A,c1_6__bvfunc_8,k6_margrel1,k1_fraenkel(c1_6__bvfunc_8,k6_margrel1))
       => c2_6__bvfunc_8 = k8_bvfunc_1(c1_6__bvfunc_8,k6_valuat_1(c1_6__bvfunc_8,c2_6__bvfunc_8,A),k6_valuat_1(c1_6__bvfunc_8,c2_6__bvfunc_8,k5_valuat_1(c1_6__bvfunc_8,A))) ) ),
    introduced(definition,[new_symbol(c3_6__bvfunc_8),file(bvfunc_8,c3_6__bvfunc_8)]),
    [interesting(0.8),axiom,file(bvfunc_8,c3_6__bvfunc_8)]).

fof(existence_m1_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m1_relset_1(C,A,B) ),
    file(relset_1,m1_relset_1),
    [interesting(0.9),axiom,file(relset_1,m1_relset_1)]).

fof(dt_k2_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k2_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,k2_zfmisc_1)]).

fof(dt_m1_relset_1,axiom,(
    $true ),
    file(relset_1,m1_relset_1),
    [interesting(0.9),axiom,file(relset_1,m1_relset_1)]).

fof(cc1_fraenkel,theorem,(
    ! [A] : 
      ( v1_fraenkel(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_relat_1(B)
            & v1_funct_1(B) ) ) ) ),
    file(fraenkel,cc1_fraenkel),
    [interesting(0.9),axiom,file(fraenkel,cc1_fraenkel)]).

fof(rc1_fraenkel,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_fraenkel(A) ) ),
    file(fraenkel,rc1_fraenkel),
    [interesting(0.9),axiom,file(fraenkel,rc1_fraenkel)]).

fof(rc1_margrel1,theorem,(
    ? [A] : v1_margrel1(A) ),
    file(margrel1,rc1_margrel1),
    [interesting(0.9),axiom,file(margrel1,rc1_margrel1)]).

fof(existence_m1_fraenkel,axiom,(
    ! [A,B] : 
    ? [C] : m1_fraenkel(C,A,B) ),
    file(fraenkel,m1_fraenkel),
    [interesting(0.9),axiom,file(fraenkel,m1_fraenkel)]).

fof(existence_m2_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m2_relset_1(C,A,B) ),
    file(relset_1,m2_relset_1),
    [interesting(0.9),axiom,file(relset_1,m2_relset_1)]).

fof(redefinition_m2_relset_1,definition,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
    <=> m1_relset_1(C,A,B) ) ),
    file(relset_1,m2_relset_1),
    [interesting(0.9),axiom,file(relset_1,m2_relset_1)]).

fof(dt_k1_funct_2,axiom,(
    $true ),
    file(funct_2,k1_funct_2),
    [interesting(0.9),axiom,file(funct_2,k1_funct_2)]).

fof(dt_k1_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k1_xboole_0)]).

fof(dt_m1_fraenkel,axiom,(
    ! [A,B,C] : 
      ( m1_fraenkel(C,A,B)
     => ( ~ v1_xboole_0(C)
        & v1_fraenkel(C) ) ) ),
    file(fraenkel,m1_fraenkel),
    [interesting(0.9),axiom,file(fraenkel,m1_fraenkel)]).

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),
    [interesting(0.9),axiom,file(relset_1,m2_relset_1)]).

fof(fc1_fraenkel,theorem,(
    ! [A,B] : v1_fraenkel(k1_funct_2(A,B)) ),
    file(fraenkel,fc1_fraenkel),
    [interesting(0.9),axiom,file(fraenkel,fc1_fraenkel)]).

fof(fc1_margrel1,theorem,
    ( v1_xboole_0(k1_xboole_0)
    & v1_margrel1(k1_xboole_0) ),
    file(margrel1,fc1_margrel1),
    [interesting(0.9),axiom,file(margrel1,fc1_margrel1)]).

fof(fc2_valuat_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_valuat_1(A) )
     => v2_margrel1(k1_funct_1(A,B)) ) ),
    file(valuat_1,fc2_valuat_1),
    [interesting(0.9),axiom,file(valuat_1,fc2_valuat_1)]).

fof(fc3_valuat_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_valuat_1(A) )
     => ( v1_relat_1(k3_valuat_1(A))
        & v1_funct_1(k3_valuat_1(A))
        & v1_valuat_1(k3_valuat_1(A)) ) ) ),
    file(valuat_1,fc3_valuat_1),
    [interesting(0.9),axiom,file(valuat_1,fc3_valuat_1)]).

fof(fc4_valuat_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_valuat_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & v1_valuat_1(B) )
     => ( v1_relat_1(k4_valuat_1(A,B))
        & v1_funct_1(k4_valuat_1(A,B))
        & v1_valuat_1(k4_valuat_1(A,B)) ) ) ),
    file(valuat_1,fc4_valuat_1),
    [interesting(0.9),axiom,file(valuat_1,fc4_valuat_1)]).

fof(rc1_valuat_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v1_valuat_1(A) ) ),
    file(valuat_1,rc1_valuat_1),
    [interesting(0.9),axiom,file(valuat_1,rc1_valuat_1)]).

fof(rc2_margrel1,theorem,(
    ? [A] : v2_margrel1(A) ),
    file(margrel1,rc2_margrel1),
    [interesting(0.9),axiom,file(margrel1,rc2_margrel1)]).

fof(commutativity_k4_valuat_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_valuat_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & v1_valuat_1(B) )
     => k4_valuat_1(A,B) = k4_valuat_1(B,A) ) ),
    file(valuat_1,k4_valuat_1),
    [interesting(0.9),axiom,file(valuat_1,k4_valuat_1)]).

fof(commutativity_k6_bvfunc_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_valuat_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & v1_valuat_1(B) )
     => k6_bvfunc_1(A,B) = k6_bvfunc_1(B,A) ) ),
    file(bvfunc_1,k6_bvfunc_1),
    [interesting(0.9),axiom,file(bvfunc_1,k6_bvfunc_1)]).

fof(existence_m1_subset_1,axiom,(
    ! [A] : 
    ? [B] : m1_subset_1(B,A) ),
    file(subset_1,m1_subset_1),
    [interesting(0.9),axiom,file(subset_1,m1_subset_1)]).

fof(existence_m2_fraenkel,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(B)
        & m1_fraenkel(C,A,B) )
     => ? [D] : m2_fraenkel(D,A,B,C) ) ),
    file(fraenkel,m2_fraenkel),
    [interesting(0.9),axiom,file(fraenkel,m2_fraenkel)]).

fof(redefinition_k1_fraenkel,definition,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => k1_fraenkel(A,B) = k1_funct_2(A,B) ) ),
    file(fraenkel,k1_fraenkel),
    [interesting(0.9),axiom,file(fraenkel,k1_fraenkel)]).

fof(redefinition_m2_fraenkel,definition,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(B)
        & m1_fraenkel(C,A,B) )
     => ! [D] : 
          ( m2_fraenkel(D,A,B,C)
        <=> m1_subset_1(D,C) ) ) ),
    file(fraenkel,m2_fraenkel),
    [interesting(0.9),axiom,file(fraenkel,m2_fraenkel)]).

fof(dt_k1_fraenkel,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => m1_fraenkel(k1_fraenkel(A,B),A,B) ) ),
    file(fraenkel,k1_fraenkel),
    [interesting(0.9),axiom,file(fraenkel,k1_fraenkel)]).

fof(dt_k1_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k1_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,k1_zfmisc_1)]).

fof(dt_k3_valuat_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_valuat_1(A) )
     => ( v1_relat_1(k3_valuat_1(A))
        & v1_funct_1(k3_valuat_1(A)) ) ) ),
    file(valuat_1,k3_valuat_1),
    [interesting(0.9),axiom,file(valuat_1,k3_valuat_1)]).

fof(dt_k4_valuat_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_valuat_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & v1_valuat_1(B) )
     => ( v1_relat_1(k4_valuat_1(A,B))
        & v1_funct_1(k4_valuat_1(A,B)) ) ) ),
    file(valuat_1,k4_valuat_1),
    [interesting(0.9),axiom,file(valuat_1,k4_valuat_1)]).

fof(dt_k6_bvfunc_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_valuat_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & v1_valuat_1(B) )
     => ( v1_relat_1(k6_bvfunc_1(A,B))
        & v1_funct_1(k6_bvfunc_1(A,B)) ) ) ),
    file(bvfunc_1,k6_bvfunc_1),
    [interesting(0.9),axiom,file(bvfunc_1,k6_bvfunc_1)]).

fof(dt_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    [interesting(0.9),axiom,file(subset_1,m1_subset_1)]).

fof(dt_m2_fraenkel,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(B)
        & m1_fraenkel(C,A,B) )
     => ! [D] : 
          ( m2_fraenkel(D,A,B,C)
         => ( v1_funct_1(D)
            & v1_funct_2(D,A,B)
            & m2_relset_1(D,A,B) ) ) ) ),
    file(fraenkel,m2_fraenkel),
    [interesting(0.9),axiom,file(fraenkel,m2_fraenkel)]).

fof(cc1_margrel1,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k6_margrel1)
     => v2_margrel1(A) ) ),
    file(margrel1,cc1_margrel1),
    [interesting(0.9),axiom,file(margrel1,cc1_margrel1)]).

fof(cc1_valuat_1,theorem,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_fraenkel(A,k6_margrel1))
     => v1_valuat_1(B) ) ),
    file(valuat_1,cc1_valuat_1),
    [interesting(0.9),axiom,file(valuat_1,cc1_valuat_1)]).

fof(t2_subset,theorem,(
    ! [A,B] : 
      ( m1_subset_1(A,B)
     => ( v1_xboole_0(B)
        | r2_hidden(A,B) ) ) ),
    file(subset,t2_subset),
    [interesting(0.9),axiom,file(subset,t2_subset)]).

fof(t4_subset,theorem,(
    ! [A,B,C] : 
      ( ( r2_hidden(A,B)
        & m1_subset_1(B,k1_zfmisc_1(C)) )
     => m1_subset_1(A,C) ) ),
    file(subset,t4_subset),
    [interesting(0.9),axiom,file(subset,t4_subset)]).

fof(t5_subset,theorem,(
    ! [A,B,C] : 
      ~ ( r2_hidden(A,B)
        & m1_subset_1(B,k1_zfmisc_1(C))
        & v1_xboole_0(C) ) ),
    file(subset,t5_subset),
    [interesting(0.9),axiom,file(subset,t5_subset)]).

fof(t6_boole,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => A = k1_xboole_0 ) ),
    file(boole,t6_boole),
    [interesting(0.9),axiom,file(boole,t6_boole)]).

fof(t8_boole,theorem,(
    ! [A,B] : 
      ~ ( v1_xboole_0(A)
        & A != B
        & v1_xboole_0(B) ) ),
    file(boole,t8_boole),
    [interesting(0.9),axiom,file(boole,t8_boole)]).

fof(commutativity_k6_valuat_1,theorem,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k1_fraenkel(A,k6_margrel1))
        & m1_subset_1(C,k1_fraenkel(A,k6_margrel1)) )
     => k6_valuat_1(A,B,C) = k6_valuat_1(A,C,B) ) ),
    file(valuat_1,k6_valuat_1),
    [interesting(0.9),axiom,file(valuat_1,k6_valuat_1)]).

fof(commutativity_k8_bvfunc_1,theorem,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k1_fraenkel(A,k6_margrel1))
        & m1_subset_1(C,k1_fraenkel(A,k6_margrel1)) )
     => k8_bvfunc_1(A,B,C) = k8_bvfunc_1(A,C,B) ) ),
    file(bvfunc_1,k8_bvfunc_1),
    [interesting(0.9),axiom,file(bvfunc_1,k8_bvfunc_1)]).

fof(reflexivity_r1_tarski,theorem,(
    ! [A,B] : r1_tarski(A,A) ),
    file(tarski,r1_tarski),
    [interesting(0.9),axiom,file(tarski,r1_tarski)]).

fof(antisymmetry_r2_hidden,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => ~ r2_hidden(B,A) ) ),
    file(hidden,r2_hidden),
    [interesting(0.9),axiom,file(hidden,r2_hidden)]).

fof(redefinition_k5_valuat_1,definition,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k1_fraenkel(A,k6_margrel1)) )
     => k5_valuat_1(A,B) = k3_valuat_1(B) ) ),
    file(valuat_1,k5_valuat_1),
    [interesting(0.9),axiom,file(valuat_1,k5_valuat_1)]).

fof(redefinition_k6_valuat_1,definition,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k1_fraenkel(A,k6_margrel1))
        & m1_subset_1(C,k1_fraenkel(A,k6_margrel1)) )
     => k6_valuat_1(A,B,C) = k4_valuat_1(B,C) ) ),
    file(valuat_1,k6_valuat_1),
    [interesting(0.9),axiom,file(valuat_1,k6_valuat_1)]).

fof(redefinition_k8_bvfunc_1,definition,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k1_fraenkel(A,k6_margrel1))
        & m1_subset_1(C,k1_fraenkel(A,k6_margrel1)) )
     => k8_bvfunc_1(A,B,C) = k6_bvfunc_1(B,C) ) ),
    file(bvfunc_1,k8_bvfunc_1),
    [interesting(0.9),axiom,file(bvfunc_1,k8_bvfunc_1)]).

fof(dt_k1_funct_1,axiom,(
    $true ),
    file(funct_1,k1_funct_1),
    [interesting(0.9),axiom,file(funct_1,k1_funct_1)]).

fof(dt_k1_relat_1,axiom,(
    $true ),
    file(relat_1,k1_relat_1),
    [interesting(0.9),axiom,file(relat_1,k1_relat_1)]).

fof(dt_k2_relat_1,axiom,(
    $true ),
    file(relat_1,k2_relat_1),
    [interesting(0.9),axiom,file(relat_1,k2_relat_1)]).

fof(dt_k5_valuat_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k1_fraenkel(A,k6_margrel1)) )
     => m2_fraenkel(k5_valuat_1(A,B),A,k6_margrel1,k1_fraenkel(A,k6_margrel1)) ) ),
    file(valuat_1,k5_valuat_1),
    [interesting(0.9),axiom,file(valuat_1,k5_valuat_1)]).

fof(dt_k6_margrel1,axiom,(
    $true ),
    file(margrel1,k6_margrel1),
    [interesting(0.9),axiom,file(margrel1,k6_margrel1)]).

fof(dt_k6_valuat_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k1_fraenkel(A,k6_margrel1))
        & m1_subset_1(C,k1_fraenkel(A,k6_margrel1)) )
     => m2_fraenkel(k6_valuat_1(A,B,C),A,k6_margrel1,k1_fraenkel(A,k6_margrel1)) ) ),
    file(valuat_1,k6_valuat_1),
    [interesting(0.9),axiom,file(valuat_1,k6_valuat_1)]).

fof(dt_k8_bvfunc_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k1_fraenkel(A,k6_margrel1))
        & m1_subset_1(C,k1_fraenkel(A,k6_margrel1)) )
     => m2_fraenkel(k8_bvfunc_1(A,B,C),A,k6_margrel1,k1_fraenkel(A,k6_margrel1)) ) ),
    file(bvfunc_1,k8_bvfunc_1),
    [interesting(0.9),axiom,file(bvfunc_1,k8_bvfunc_1)]).

fof(dt_c1_6__bvfunc_8,assumption,(
    ~ v1_xboole_0(c1_6__bvfunc_8) ),
    introduced(assumption,[file(bvfunc_8,c1_6__bvfunc_8)]),
    [interesting(0.8),axiom,file(bvfunc_8,c1_6__bvfunc_8)]).

fof(dt_c2_6__bvfunc_8,assumption,(
    m2_fraenkel(c2_6__bvfunc_8,c1_6__bvfunc_8,k6_margrel1,k1_fraenkel(c1_6__bvfunc_8,k6_margrel1)) ),
    introduced(assumption,[file(bvfunc_8,c2_6__bvfunc_8)]),
    [interesting(0.8),axiom,file(bvfunc_8,c2_6__bvfunc_8)]).

fof(dt_c3_6__bvfunc_8,assumption,(
    m2_fraenkel(c3_6__bvfunc_8,c1_6__bvfunc_8,k6_margrel1,k1_fraenkel(c1_6__bvfunc_8,k6_margrel1)) ),
    introduced(assumption,[file(bvfunc_8,c3_6__bvfunc_8)]),
    [interesting(0.8),axiom,file(bvfunc_8,c3_6__bvfunc_8)]).

fof(dh_c4_6__bvfunc_8,definition,
    ( ? [A] : 
        ( v1_relat_1(A)
        & v1_funct_1(A)
        & c2_6__bvfunc_8 = A
        & k1_relat_1(A) = c1_6__bvfunc_8
        & r1_tarski(k2_relat_1(A),k6_margrel1) )
   => ( v1_relat_1(c4_6__bvfunc_8)
      & v1_funct_1(c4_6__bvfunc_8)
      & c2_6__bvfunc_8 = c4_6__bvfunc_8
      & k1_relat_1(c4_6__bvfunc_8) = c1_6__bvfunc_8
      & r1_tarski(k2_relat_1(c4_6__bvfunc_8),k6_margrel1) ) ),
    introduced(definition,[new_symbol(c4_6__bvfunc_8),file(bvfunc_8,c4_6__bvfunc_8)]),
    [interesting(0.8),axiom,file(bvfunc_8,c4_6__bvfunc_8)]).

fof(fc3_margrel1,theorem,(
    ~ v1_xboole_0(k6_margrel1) ),
    file(margrel1,fc3_margrel1),
    [interesting(0.9),axiom,file(margrel1,fc3_margrel1)]).

fof(t1_subset,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => m1_subset_1(A,B) ) ),
    file(subset,t1_subset),
    [interesting(0.9),axiom,file(subset,t1_subset)]).

fof(t3_subset,theorem,(
    ! [A,B] : 
      ( m1_subset_1(A,k1_zfmisc_1(B))
    <=> r1_tarski(A,B) ) ),
    file(subset,t3_subset),
    [interesting(0.9),axiom,file(subset,t3_subset)]).

fof(t7_boole,theorem,(
    ! [A,B] : 
      ~ ( r2_hidden(A,B)
        & v1_xboole_0(B) ) ),
    file(boole,t7_boole),
    [interesting(0.9),axiom,file(boole,t7_boole)]).

fof(d2_funct_2,definition,(
    ! [A,B,C] : 
      ( C = k1_funct_2(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ? [E] : 
              ( v1_relat_1(E)
              & v1_funct_1(E)
              & D = E
              & k1_relat_1(E) = A
              & r1_tarski(k2_relat_1(E),B) ) ) ) ),
    file(funct_2,d2_funct_2),
    [interesting(0.9),axiom,file(funct_2,d2_funct_2)]).

fof(e2_6__bvfunc_8,plain,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & c2_6__bvfunc_8 = A
      & k1_relat_1(A) = c1_6__bvfunc_8
      & r1_tarski(k2_relat_1(A),k6_margrel1) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6__bvfunc_8,dt_c2_6__bvfunc_8])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,rc1_margrel1,existence_m1_fraenkel,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_m1_fraenkel,dt_m2_relset_1,fc1_margrel1,rc1_valuat_1,rc2_margrel1,existence_m1_subset_1,existence_m2_fraenkel,redefinition_k1_fraenkel,redefinition_m2_fraenkel,dt_k1_fraenkel,dt_k1_zfmisc_1,dt_m1_subset_1,dt_m2_fraenkel,cc1_fraenkel,cc1_margrel1,cc1_valuat_1,rc1_fraenkel,t2_subset,t4_subset,t5_subset,t6_boole,t8_boole,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_funct_2,dt_k1_relat_1,dt_k2_relat_1,dt_k6_margrel1,dt_c1_6__bvfunc_8,dt_c2_6__bvfunc_8,fc1_fraenkel,fc3_margrel1,t1_subset,t3_subset,t7_boole,d2_funct_2]),
    [interesting(0.8),file(bvfunc_8,e2_6__bvfunc_8),[file(bvfunc_8,e2_6__bvfunc_8)]]).

fof(dt_c4_6__bvfunc_8,plain,
    ( v1_relat_1(c4_6__bvfunc_8)
    & v1_funct_1(c4_6__bvfunc_8) ),
    inference(consider,[status(thm),assumptions([dt_c1_6__bvfunc_8,dt_c2_6__bvfunc_8])],[dh_c4_6__bvfunc_8,e2_6__bvfunc_8]),
    [interesting(0.8),file(bvfunc_8,c4_6__bvfunc_8),[file(bvfunc_8,c4_6__bvfunc_8)]]).

fof(dh_c5_6__bvfunc_8,definition,
    ( ? [A] : 
        ( v1_relat_1(A)
        & v1_funct_1(A)
        & k8_bvfunc_1(c1_6__bvfunc_8,k6_valuat_1(c1_6__bvfunc_8,c2_6__bvfunc_8,c3_6__bvfunc_8),k6_valuat_1(c1_6__bvfunc_8,c2_6__bvfunc_8,k5_valuat_1(c1_6__bvfunc_8,c3_6__bvfunc_8))) = A
        & k1_relat_1(A) = c1_6__bvfunc_8
        & r1_tarski(k2_relat_1(A),k6_margrel1) )
   => ( v1_relat_1(c5_6__bvfunc_8)
      & v1_funct_1(c5_6__bvfunc_8)
      & k8_bvfunc_1(c1_6__bvfunc_8,k6_valuat_1(c1_6__bvfunc_8,c2_6__bvfunc_8,c3_6__bvfunc_8),k6_valuat_1(c1_6__bvfunc_8,c2_6__bvfunc_8,k5_valuat_1(c1_6__bvfunc_8,c3_6__bvfunc_8))) = c5_6__bvfunc_8
      & k1_relat_1(c5_6__bvfunc_8) = c1_6__bvfunc_8
      & r1_tarski(k2_relat_1(c5_6__bvfunc_8),k6_margrel1) ) ),
    introduced(definition,[new_symbol(c5_6__bvfunc_8),file(bvfunc_8,c5_6__bvfunc_8)]),
    [interesting(0.8),axiom,file(bvfunc_8,c5_6__bvfunc_8)]).

fof(e4_6__bvfunc_8,plain,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & k8_bvfunc_1(c1_6__bvfunc_8,k6_valuat_1(c1_6__bvfunc_8,c2_6__bvfunc_8,c3_6__bvfunc_8),k6_valuat_1(c1_6__bvfunc_8,c2_6__bvfunc_8,k5_valuat_1(c1_6__bvfunc_8,c3_6__bvfunc_8))) = A
      & k1_relat_1(A) = c1_6__bvfunc_8
      & r1_tarski(k2_relat_1(A),k6_margrel1) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6__bvfunc_8,dt_c2_6__bvfunc_8,dt_c3_6__bvfunc_8])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,rc1_margrel1,existence_m1_fraenkel,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_m1_fraenkel,dt_m2_relset_1,fc1_margrel1,fc3_valuat_1,fc4_valuat_1,rc1_valuat_1,rc2_margrel1,commutativity_k4_valuat_1,commutativity_k6_bvfunc_1,existence_m1_subset_1,existence_m2_fraenkel,redefinition_k1_fraenkel,redefinition_m2_fraenkel,dt_k1_fraenkel,dt_k1_zfmisc_1,dt_k3_valuat_1,dt_k4_valuat_1,dt_k6_bvfunc_1,dt_m1_subset_1,dt_m2_fraenkel,cc1_fraenkel,cc1_margrel1,cc1_valuat_1,rc1_fraenkel,t2_subset,t4_subset,t5_subset,t6_boole,t8_boole,commutativity_k6_valuat_1,commutativity_k8_bvfunc_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,redefinition_k5_valuat_1,redefinition_k6_valuat_1,redefinition_k8_bvfunc_1,dt_k1_funct_2,dt_k1_relat_1,dt_k2_relat_1,dt_k5_valuat_1,dt_k6_margrel1,dt_k6_valuat_1,dt_k8_bvfunc_1,dt_c1_6__bvfunc_8,dt_c2_6__bvfunc_8,dt_c3_6__bvfunc_8,fc1_fraenkel,fc3_margrel1,t1_subset,t3_subset,t7_boole,d2_funct_2]),
    [interesting(0.8),file(bvfunc_8,e4_6__bvfunc_8),[file(bvfunc_8,e4_6__bvfunc_8)]]).

fof(dt_c5_6__bvfunc_8,plain,
    ( v1_relat_1(c5_6__bvfunc_8)
    & v1_funct_1(c5_6__bvfunc_8) ),
    inference(consider,[status(thm),assumptions([dt_c1_6__bvfunc_8,dt_c2_6__bvfunc_8,dt_c3_6__bvfunc_8])],[dh_c5_6__bvfunc_8,e4_6__bvfunc_8]),
    [interesting(0.8),file(bvfunc_8,c5_6__bvfunc_8),[file(bvfunc_8,c5_6__bvfunc_8)]]).

fof(dh_c1_6_1__bvfunc_8,definition,
    ( ( m1_subset_1(c1_6_1__bvfunc_8,c1_6__bvfunc_8)
     => k1_funct_1(c2_6__bvfunc_8,c1_6_1__bvfunc_8) = k1_funct_1(k8_bvfunc_1(c1_6__bvfunc_8,k6_valuat_1(c1_6__bvfunc_8,c2_6__bvfunc_8,c3_6__bvfunc_8),k6_valuat_1(c1_6__bvfunc_8,c2_6__bvfunc_8,k5_valuat_1(c1_6__bvfunc_8,c3_6__bvfunc_8))),c1_6_1__bvfunc_8) )
   => ! [A] : 
        ( m1_subset_1(A,c1_6__bvfunc_8)
       => k1_funct_1(c2_6__bvfunc_8,A) = k1_funct_1(k8_bvfunc_1(c1_6__bvfunc_8,k6_valuat_1(c1_6__bvfunc_8,c2_6__bvfunc_8,c3_6__bvfunc_8),k6_valuat_1(c1_6__bvfunc_8,c2_6__bvfunc_8,k5_valuat_1(c1_6__bvfunc_8,c3_6__bvfunc_8))),A) ) ),
    introduced(definition,[new_symbol(c1_6_1__bvfunc_8),file(bvfunc_8,c1_6_1__bvfunc_8)]),
    [interesting(0.65),axiom,file(bvfunc_8,c1_6_1__bvfunc_8)]).

fof(dt_c1_6_1__bvfunc_8,assumption,(
    m1_subset_1(c1_6_1__bvfunc_8,c1_6__bvfunc_8) ),
    introduced(assumption,[file(bvfunc_8,c1_6_1__bvfunc_8)]),
    [interesting(0.65),axiom,file(bvfunc_8,c1_6_1__bvfunc_8)]).

fof(t15_bvfunc_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] : 
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] : 
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => k6_valuat_1(A,k8_bvfunc_1(A,B,C),D) = k8_bvfunc_1(A,k6_valuat_1(A,B,D),k6_valuat_1(A,C,D)) ) ) ) ) ),
    file(bvfunc_1,t15_bvfunc_1),
    [interesting(0.9),axiom,file(bvfunc_1,t15_bvfunc_1)]).

fof(e1_6_1_1__bvfunc_8,plain,(
    k1_funct_1(k8_bvfunc_1(c1_6__bvfunc_8,k6_valuat_1(c1_6__bvfunc_8,c2_6__bvfunc_8,c3_6__bvfunc_8),k6_valuat_1(c1_6__bvfunc_8,c2_6__bvfunc_8,k5_valuat_1(c1_6__bvfunc_8,c3_6__bvfunc_8))),c1_6_1__bvfunc_8) = k1_funct_1(k6_valuat_1(c1_6__bvfunc_8,c2_6__bvfunc_8,k8_bvfunc_1(c1_6__bvfunc_8,c3_6__bvfunc_8,k5_valuat_1(c1_6__bvfunc_8,c3_6__bvfunc_8))),c1_6_1__bvfunc_8) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6__bvfunc_8,dt_c1_6_1__bvfunc_8,dt_c2_6__bvfunc_8,dt_c3_6__bvfunc_8])],[reflexivity_r1_tarski,existence_m1_relset_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_fraenkel,fc2_valuat_1,fc3_valuat_1,fc4_valuat_1,rc1_fraenkel,rc1_margrel1,rc1_valuat_1,rc2_margrel1,t3_subset,t4_subset,t5_subset,commutativity_k4_valuat_1,commutativity_k6_bvfunc_1,antisymmetry_r2_hidden,existence_m1_fraenkel,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_funct_2,dt_k1_xboole_0,dt_k3_valuat_1,dt_k4_valuat_1,dt_k6_bvfunc_1,dt_m1_fraenkel,dt_m1_subset_1,dt_m2_relset_1,cc1_margrel1,cc1_valuat_1,fc1_fraenkel,fc1_margrel1,t1_subset,t2_subset,commutativity_k6_valuat_1,commutativity_k8_bvfunc_1,existence_m2_fraenkel,redefinition_k1_fraenkel,redefinition_k5_valuat_1,redefinition_k6_valuat_1,redefinition_k8_bvfunc_1,redefinition_m2_fraenkel,dt_k1_fraenkel,dt_k1_funct_1,dt_k5_valuat_1,dt_k6_margrel1,dt_k6_valuat_1,dt_k8_bvfunc_1,dt_m2_fraenkel,dt_c1_6__bvfunc_8,dt_c1_6_1__bvfunc_8,dt_c2_6__bvfunc_8,dt_c3_6__bvfunc_8,fc3_margrel1,t6_boole,t7_boole,t8_boole,t15_bvfunc_1]),
    [interesting(0.5),file(bvfunc_8,e1_6_1_1__bvfunc_8),[file(bvfunc_8,e1_6_1_1__bvfunc_8)]]).

fof(dt_k19_bvfunc_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => m2_fraenkel(k19_bvfunc_1(A),A,k6_margrel1,k1_fraenkel(A,k6_margrel1)) ) ),
    file(bvfunc_1,k19_bvfunc_1),
    [interesting(0.9),axiom,file(bvfunc_1,k19_bvfunc_1)]).

fof(t6_bvfunc_4,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => k8_bvfunc_1(A,B,k5_valuat_1(A,B)) = k19_bvfunc_1(A) ) ) ),
    file(bvfunc_4,t6_bvfunc_4),
    [interesting(0.9),axiom,file(bvfunc_4,t6_bvfunc_4)]).

fof(e2_6_1_1__bvfunc_8,plain,(
    k1_funct_1(k6_valuat_1(c1_6__bvfunc_8,c2_6__bvfunc_8,k8_bvfunc_1(c1_6__bvfunc_8,c3_6__bvfunc_8,k5_valuat_1(c1_6__bvfunc_8,c3_6__bvfunc_8))),c1_6_1__bvfunc_8) = k1_funct_1(k6_valuat_1(c1_6__bvfunc_8,c2_6__bvfunc_8,k19_bvfunc_1(c1_6__bvfunc_8)),c1_6_1__bvfunc_8) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6__bvfunc_8,dt_c1_6_1__bvfunc_8,dt_c2_6__bvfunc_8,dt_c3_6__bvfunc_8])],[reflexivity_r1_tarski,existence_m1_relset_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_fraenkel,fc2_valuat_1,fc3_valuat_1,fc4_valuat_1,rc1_fraenkel,rc1_margrel1,rc1_valuat_1,rc2_margrel1,t3_subset,t4_subset,t5_subset,commutativity_k4_valuat_1,commutativity_k6_bvfunc_1,antisymmetry_r2_hidden,existence_m1_fraenkel,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_funct_2,dt_k1_xboole_0,dt_k3_valuat_1,dt_k4_valuat_1,dt_k6_bvfunc_1,dt_m1_fraenkel,dt_m1_subset_1,dt_m2_relset_1,cc1_margrel1,cc1_valuat_1,fc1_fraenkel,fc1_margrel1,t1_subset,t2_subset,commutativity_k6_valuat_1,commutativity_k8_bvfunc_1,existence_m2_fraenkel,redefinition_k1_fraenkel,redefinition_k5_valuat_1,redefinition_k6_valuat_1,redefinition_k8_bvfunc_1,redefinition_m2_fraenkel,dt_k19_bvfunc_1,dt_k1_fraenkel,dt_k1_funct_1,dt_k5_valuat_1,dt_k6_margrel1,dt_k6_valuat_1,dt_k8_bvfunc_1,dt_m2_fraenkel,dt_c1_6__bvfunc_8,dt_c1_6_1__bvfunc_8,dt_c2_6__bvfunc_8,dt_c3_6__bvfunc_8,fc3_margrel1,t6_boole,t7_boole,t8_boole,t6_bvfunc_4]),
    [interesting(0.5),file(bvfunc_8,e2_6_1_1__bvfunc_8),[file(bvfunc_8,e2_6_1_1__bvfunc_8)]]).

fof(t9_bvfunc_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => k6_valuat_1(A,B,k19_bvfunc_1(A)) = B ) ) ),
    file(bvfunc_1,t9_bvfunc_1),
    [interesting(0.9),axiom,file(bvfunc_1,t9_bvfunc_1)]).

fof(e3_6_1_1__bvfunc_8,plain,(
    k1_funct_1(k6_valuat_1(c1_6__bvfunc_8,c2_6__bvfunc_8,k19_bvfunc_1(c1_6__bvfunc_8)),c1_6_1__bvfunc_8) = k1_funct_1(c2_6__bvfunc_8,c1_6_1__bvfunc_8) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6__bvfunc_8,dt_c1_6_1__bvfunc_8,dt_c2_6__bvfunc_8])],[reflexivity_r1_tarski,existence_m1_relset_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_fraenkel,fc2_valuat_1,fc4_valuat_1,rc1_fraenkel,rc1_margrel1,rc1_valuat_1,rc2_margrel1,t3_subset,t4_subset,t5_subset,commutativity_k4_valuat_1,antisymmetry_r2_hidden,existence_m1_fraenkel,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_funct_2,dt_k1_xboole_0,dt_k4_valuat_1,dt_m1_fraenkel,dt_m1_subset_1,dt_m2_relset_1,cc1_margrel1,cc1_valuat_1,fc1_fraenkel,fc1_margrel1,t1_subset,t2_subset,commutativity_k6_valuat_1,existence_m2_fraenkel,redefinition_k1_fraenkel,redefinition_k6_valuat_1,redefinition_m2_fraenkel,dt_k19_bvfunc_1,dt_k1_fraenkel,dt_k1_funct_1,dt_k6_margrel1,dt_k6_valuat_1,dt_m2_fraenkel,dt_c1_6__bvfunc_8,dt_c1_6_1__bvfunc_8,dt_c2_6__bvfunc_8,fc3_margrel1,t6_boole,t7_boole,t8_boole,t9_bvfunc_1]),
    [interesting(0.5),file(bvfunc_8,e3_6_1_1__bvfunc_8),[file(bvfunc_8,e3_6_1_1__bvfunc_8)]]).

fof(e1_6_1__bvfunc_8,plain,(
    k1_funct_1(k8_bvfunc_1(c1_6__bvfunc_8,k6_valuat_1(c1_6__bvfunc_8,c2_6__bvfunc_8,c3_6__bvfunc_8),k6_valuat_1(c1_6__bvfunc_8,c2_6__bvfunc_8,k5_valuat_1(c1_6__bvfunc_8,c3_6__bvfunc_8))),c1_6_1__bvfunc_8) = k1_funct_1(c2_6__bvfunc_8,c1_6_1__bvfunc_8) ),
    inference(iterative_eq,[status(thm),assumptions([dt_c3_6__bvfunc_8,dt_c1_6__bvfunc_8,dt_c1_6_1__bvfunc_8,dt_c2_6__bvfunc_8])],[e1_6_1_1__bvfunc_8,e2_6_1_1__bvfunc_8,e3_6_1_1__bvfunc_8]),
    [interesting(0.65),file(bvfunc_8,e1_6_1__bvfunc_8),[file(bvfunc_8,e1_6_1__bvfunc_8)]]).

fof(e2_6_1__bvfunc_8,plain,(
    k1_funct_1(c2_6__bvfunc_8,c1_6_1__bvfunc_8) = k1_funct_1(k8_bvfunc_1(c1_6__bvfunc_8,k6_valuat_1(c1_6__bvfunc_8,c2_6__bvfunc_8,c3_6__bvfunc_8),k6_valuat_1(c1_6__bvfunc_8,c2_6__bvfunc_8,k5_valuat_1(c1_6__bvfunc_8,c3_6__bvfunc_8))),c1_6_1__bvfunc_8) ),
    inference(mizar_by,[status(thm),assumptions([dt_c3_6__bvfunc_8,dt_c1_6__bvfunc_8,dt_c1_6_1__bvfunc_8,dt_c2_6__bvfunc_8])],[reflexivity_r1_tarski,existence_m1_relset_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_fraenkel,rc1_fraenkel,rc1_margrel1,t3_subset,t4_subset,t5_subset,antisymmetry_r2_hidden,existence_m1_fraenkel,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_funct_2,dt_k1_xboole_0,dt_m1_fraenkel,dt_m2_relset_1,fc1_fraenkel,fc1_margrel1,fc2_valuat_1,fc3_valuat_1,fc4_valuat_1,rc1_valuat_1,rc2_margrel1,t1_subset,commutativity_k4_valuat_1,commutativity_k6_bvfunc_1,existence_m1_subset_1,existence_m2_fraenkel,redefinition_k1_fraenkel,redefinition_m2_fraenkel,dt_k1_fraenkel,dt_k3_valuat_1,dt_k4_valuat_1,dt_k6_bvfunc_1,dt_k6_margrel1,dt_m1_subset_1,dt_m2_fraenkel,cc1_margrel1,cc1_valuat_1,fc3_margrel1,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k6_valuat_1,commutativity_k8_bvfunc_1,redefinition_k5_valuat_1,redefinition_k6_valuat_1,redefinition_k8_bvfunc_1,dt_k1_funct_1,dt_k5_valuat_1,dt_k6_valuat_1,dt_k8_bvfunc_1,dt_c1_6__bvfunc_8,dt_c1_6_1__bvfunc_8,dt_c2_6__bvfunc_8,dt_c3_6__bvfunc_8,e1_6_1__bvfunc_8]),
    [interesting(0.65),file(bvfunc_8,e2_6_1__bvfunc_8),[file(bvfunc_8,e2_6_1__bvfunc_8)]]).

fof(i2_6_1__bvfunc_8,theorem,(
    $true ),
    introduced(tautology,[file(bvfunc_8,i2_6_1__bvfunc_8)]),
    [interesting(0.65),trivial,file(bvfunc_8,i2_6_1__bvfunc_8)]).

fof(i1_6_1__bvfunc_8,plain,(
    k1_funct_1(c2_6__bvfunc_8,c1_6_1__bvfunc_8) = k1_funct_1(k8_bvfunc_1(c1_6__bvfunc_8,k6_valuat_1(c1_6__bvfunc_8,c2_6__bvfunc_8,c3_6__bvfunc_8),k6_valuat_1(c1_6__bvfunc_8,c2_6__bvfunc_8,k5_valuat_1(c1_6__bvfunc_8,c3_6__bvfunc_8))),c1_6_1__bvfunc_8) ),
    inference(conclusion,[status(thm),assumptions([dt_c3_6__bvfunc_8,dt_c1_6__bvfunc_8,dt_c1_6_1__bvfunc_8,dt_c2_6__bvfunc_8])],[e2_6_1__bvfunc_8,i2_6_1__bvfunc_8]),
    [interesting(0.65),file(bvfunc_8,i1_6_1__bvfunc_8),[file(bvfunc_8,i1_6_1__bvfunc_8)]]).

fof(i1_6_1_tmp__bvfunc_8,plain,
    ( m1_subset_1(c1_6_1__bvfunc_8,c1_6__bvfunc_8)
   => k1_funct_1(c2_6__bvfunc_8,c1_6_1__bvfunc_8) = k1_funct_1(k8_bvfunc_1(c1_6__bvfunc_8,k6_valuat_1(c1_6__bvfunc_8,c2_6__bvfunc_8,c3_6__bvfunc_8),k6_valuat_1(c1_6__bvfunc_8,c2_6__bvfunc_8,k5_valuat_1(c1_6__bvfunc_8,c3_6__bvfunc_8))),c1_6_1__bvfunc_8) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c3_6__bvfunc_8,dt_c1_6__bvfunc_8,dt_c2_6__bvfunc_8]),discharge_asm(discharge,[dt_c1_6_1__bvfunc_8])],[dt_c1_6_1__bvfunc_8,i1_6_1__bvfunc_8]),
    [interesting(0.8),e1_6__bvfunc_8]).

fof(e1_6__bvfunc_8,plain,(
    ! [A] : 
      ( m1_subset_1(A,c1_6__bvfunc_8)
     => k1_funct_1(c2_6__bvfunc_8,A) = k1_funct_1(k8_bvfunc_1(c1_6__bvfunc_8,k6_valuat_1(c1_6__bvfunc_8,c2_6__bvfunc_8,c3_6__bvfunc_8),k6_valuat_1(c1_6__bvfunc_8,c2_6__bvfunc_8,k5_valuat_1(c1_6__bvfunc_8,c3_6__bvfunc_8))),A) ) ),
    inference(let,[status(thm),assumptions([dt_c3_6__bvfunc_8,dt_c1_6__bvfunc_8,dt_c2_6__bvfunc_8])],[i1_6_1_tmp__bvfunc_8,dh_c1_6_1__bvfunc_8]),
    [interesting(0.8),file(bvfunc_8,e1_6__bvfunc_8),[file(bvfunc_8,e1_6__bvfunc_8)]]).

fof(e3_6__bvfunc_8,plain,
    ( c2_6__bvfunc_8 = c4_6__bvfunc_8
    & k1_relat_1(c4_6__bvfunc_8) = c1_6__bvfunc_8
    & r1_tarski(k2_relat_1(c4_6__bvfunc_8),k6_margrel1) ),
    inference(consider,[status(thm),assumptions([dt_c1_6__bvfunc_8,dt_c2_6__bvfunc_8])],[dh_c4_6__bvfunc_8,e2_6__bvfunc_8]),
    [interesting(0.8),file(bvfunc_8,e3_6__bvfunc_8),[file(bvfunc_8,e3_6__bvfunc_8)]]).

fof(e5_6__bvfunc_8,plain,
    ( k8_bvfunc_1(c1_6__bvfunc_8,k6_valuat_1(c1_6__bvfunc_8,c2_6__bvfunc_8,c3_6__bvfunc_8),k6_valuat_1(c1_6__bvfunc_8,c2_6__bvfunc_8,k5_valuat_1(c1_6__bvfunc_8,c3_6__bvfunc_8))) = c5_6__bvfunc_8
    & k1_relat_1(c5_6__bvfunc_8) = c1_6__bvfunc_8
    & r1_tarski(k2_relat_1(c5_6__bvfunc_8),k6_margrel1) ),
    inference(consider,[status(thm),assumptions([dt_c1_6__bvfunc_8,dt_c2_6__bvfunc_8,dt_c3_6__bvfunc_8])],[dh_c5_6__bvfunc_8,e4_6__bvfunc_8]),
    [interesting(0.8),file(bvfunc_8,e5_6__bvfunc_8),[file(bvfunc_8,e5_6__bvfunc_8)]]).

fof(e6_6__bvfunc_8,plain,
    ( c1_6__bvfunc_8 = k1_relat_1(c4_6__bvfunc_8)
    & c1_6__bvfunc_8 = k1_relat_1(c5_6__bvfunc_8)
    & ! [A] : 
        ( r2_hidden(A,c1_6__bvfunc_8)
       => k1_funct_1(c4_6__bvfunc_8,A) = k1_funct_1(c5_6__bvfunc_8,A) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6__bvfunc_8,dt_c2_6__bvfunc_8,dt_c3_6__bvfunc_8])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_fraenkel,rc1_fraenkel,rc1_margrel1,existence_m1_fraenkel,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_funct_2,dt_k1_xboole_0,dt_m1_fraenkel,dt_m2_relset_1,fc1_fraenkel,fc1_margrel1,fc2_valuat_1,fc3_valuat_1,fc4_valuat_1,rc1_valuat_1,commutativity_k4_valuat_1,commutativity_k6_bvfunc_1,existence_m2_fraenkel,redefinition_k1_fraenkel,redefinition_m2_fraenkel,dt_k1_fraenkel,dt_k1_zfmisc_1,dt_k3_valuat_1,dt_k4_valuat_1,dt_k6_bvfunc_1,dt_m2_fraenkel,cc1_valuat_1,rc2_margrel1,t2_subset,t4_subset,t5_subset,t6_boole,t8_boole,commutativity_k6_valuat_1,commutativity_k8_bvfunc_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_m1_subset_1,redefinition_k5_valuat_1,redefinition_k6_valuat_1,redefinition_k8_bvfunc_1,dt_k1_funct_1,dt_k1_relat_1,dt_k2_relat_1,dt_k5_valuat_1,dt_k6_margrel1,dt_k6_valuat_1,dt_k8_bvfunc_1,dt_m1_subset_1,dt_c1_6__bvfunc_8,dt_c2_6__bvfunc_8,dt_c3_6__bvfunc_8,dt_c4_6__bvfunc_8,dt_c5_6__bvfunc_8,cc1_margrel1,fc3_margrel1,t1_subset,t3_subset,t7_boole,e1_6__bvfunc_8,e3_6__bvfunc_8,e5_6__bvfunc_8]),
    [interesting(0.8),file(bvfunc_8,e6_6__bvfunc_8),[file(bvfunc_8,e6_6__bvfunc_8)]]).

fof(t9_funct_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( ( k1_relat_1(A) = k1_relat_1(B)
              & ! [C] : 
                  ( r2_hidden(C,k1_relat_1(A))
                 => k1_funct_1(A,C) = k1_funct_1(B,C) ) )
           => A = B ) ) ) ),
    file(funct_1,t9_funct_1),
    [interesting(0.9),axiom,file(funct_1,t9_funct_1)]).

fof(e7_6__bvfunc_8,plain,(
    c2_6__bvfunc_8 = k8_bvfunc_1(c1_6__bvfunc_8,k6_valuat_1(c1_6__bvfunc_8,c2_6__bvfunc_8,c3_6__bvfunc_8),k6_valuat_1(c1_6__bvfunc_8,c2_6__bvfunc_8,k5_valuat_1(c1_6__bvfunc_8,c3_6__bvfunc_8))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6__bvfunc_8,dt_c2_6__bvfunc_8,dt_c3_6__bvfunc_8])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_fraenkel,rc1_fraenkel,rc1_margrel1,existence_m1_fraenkel,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_funct_2,dt_k1_xboole_0,dt_m1_fraenkel,dt_m2_relset_1,fc1_fraenkel,fc1_margrel1,fc2_valuat_1,fc3_valuat_1,fc4_valuat_1,rc1_valuat_1,rc2_margrel1,commutativity_k4_valuat_1,commutativity_k6_bvfunc_1,existence_m1_subset_1,existence_m2_fraenkel,redefinition_k1_fraenkel,redefinition_m2_fraenkel,dt_k1_fraenkel,dt_k1_zfmisc_1,dt_k3_valuat_1,dt_k4_valuat_1,dt_k6_bvfunc_1,dt_m1_subset_1,dt_m2_fraenkel,cc1_margrel1,cc1_valuat_1,t2_subset,t4_subset,t5_subset,t6_boole,t8_boole,commutativity_k6_valuat_1,commutativity_k8_bvfunc_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,redefinition_k5_valuat_1,redefinition_k6_valuat_1,redefinition_k8_bvfunc_1,dt_k1_funct_1,dt_k1_relat_1,dt_k2_relat_1,dt_k5_valuat_1,dt_k6_margrel1,dt_k6_valuat_1,dt_k8_bvfunc_1,dt_c1_6__bvfunc_8,dt_c2_6__bvfunc_8,dt_c3_6__bvfunc_8,dt_c4_6__bvfunc_8,dt_c5_6__bvfunc_8,fc3_margrel1,t1_subset,t3_subset,t7_boole,e6_6__bvfunc_8,e3_6__bvfunc_8,e5_6__bvfunc_8,t9_funct_1]),
    [interesting(0.8),file(bvfunc_8,e7_6__bvfunc_8),[file(bvfunc_8,e7_6__bvfunc_8)]]).

fof(i3_6__bvfunc_8,theorem,(
    $true ),
    introduced(tautology,[file(bvfunc_8,i3_6__bvfunc_8)]),
    [interesting(0.8),trivial,file(bvfunc_8,i3_6__bvfunc_8)]).

fof(i2_6__bvfunc_8,plain,(
    c2_6__bvfunc_8 = k8_bvfunc_1(c1_6__bvfunc_8,k6_valuat_1(c1_6__bvfunc_8,c2_6__bvfunc_8,c3_6__bvfunc_8),k6_valuat_1(c1_6__bvfunc_8,c2_6__bvfunc_8,k5_valuat_1(c1_6__bvfunc_8,c3_6__bvfunc_8))) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_6__bvfunc_8,dt_c2_6__bvfunc_8,dt_c3_6__bvfunc_8])],[e7_6__bvfunc_8,i3_6__bvfunc_8]),
    [interesting(0.8),file(bvfunc_8,i2_6__bvfunc_8),[file(bvfunc_8,i2_6__bvfunc_8)]]).

fof(i2_6_tmp__bvfunc_8,plain,
    ( ( m2_fraenkel(c2_6__bvfunc_8,c1_6__bvfunc_8,k6_margrel1,k1_fraenkel(c1_6__bvfunc_8,k6_margrel1))
      & m2_fraenkel(c3_6__bvfunc_8,c1_6__bvfunc_8,k6_margrel1,k1_fraenkel(c1_6__bvfunc_8,k6_margrel1)) )
   => c2_6__bvfunc_8 = k8_bvfunc_1(c1_6__bvfunc_8,k6_valuat_1(c1_6__bvfunc_8,c2_6__bvfunc_8,c3_6__bvfunc_8),k6_valuat_1(c1_6__bvfunc_8,c2_6__bvfunc_8,k5_valuat_1(c1_6__bvfunc_8,c3_6__bvfunc_8))) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_6__bvfunc_8]),discharge_asm(discharge,[dt_c2_6__bvfunc_8,dt_c3_6__bvfunc_8])],[dt_c2_6__bvfunc_8,dt_c3_6__bvfunc_8,i2_6__bvfunc_8]),
    [interesting(0.8),i1_6__bvfunc_8]).

fof(i1_6__bvfunc_8,plain,(
    ! [A] : 
      ( m2_fraenkel(A,c1_6__bvfunc_8,k6_margrel1,k1_fraenkel(c1_6__bvfunc_8,k6_margrel1))
     => ! [B] : 
          ( m2_fraenkel(B,c1_6__bvfunc_8,k6_margrel1,k1_fraenkel(c1_6__bvfunc_8,k6_margrel1))
         => A = k8_bvfunc_1(c1_6__bvfunc_8,k6_valuat_1(c1_6__bvfunc_8,A,B),k6_valuat_1(c1_6__bvfunc_8,A,k5_valuat_1(c1_6__bvfunc_8,B))) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_6__bvfunc_8])],[i2_6_tmp__bvfunc_8,dh_c2_6__bvfunc_8,dh_c3_6__bvfunc_8]),
    [interesting(0.8),file(bvfunc_8,i1_6__bvfunc_8),[file(bvfunc_8,i1_6__bvfunc_8)]]).

fof(i1_6_tmp__bvfunc_8,plain,
    ( ~ v1_xboole_0(c1_6__bvfunc_8)
   => ! [A] : 
        ( m2_fraenkel(A,c1_6__bvfunc_8,k6_margrel1,k1_fraenkel(c1_6__bvfunc_8,k6_margrel1))
       => ! [B] : 
            ( m2_fraenkel(B,c1_6__bvfunc_8,k6_margrel1,k1_fraenkel(c1_6__bvfunc_8,k6_margrel1))
           => A = k8_bvfunc_1(c1_6__bvfunc_8,k6_valuat_1(c1_6__bvfunc_8,A,B),k6_valuat_1(c1_6__bvfunc_8,A,k5_valuat_1(c1_6__bvfunc_8,B))) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_6__bvfunc_8])],[dt_c1_6__bvfunc_8,i1_6__bvfunc_8]),
    [interesting(1),t6_bvfunc_8]).

fof(t6_bvfunc_8,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] : 
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => B = k8_bvfunc_1(A,k6_valuat_1(A,B,C),k6_valuat_1(A,B,k5_valuat_1(A,C))) ) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_6_tmp__bvfunc_8,dh_c1_6__bvfunc_8]),
    [interesting(1),file(bvfunc_8,t6_bvfunc_8),[file(bvfunc_8,t6_bvfunc_8)]]).