% Mizar ND problem: t6_bvfunc_4,bvfunc_4,176,21 
fof(dh_c1_6__bvfunc_4,definition,
    ( ( ~ v1_xboole_0(c1_6__bvfunc_4)
     => ! [A] : 
          ( m2_fraenkel(A,c1_6__bvfunc_4,k6_margrel1,k1_fraenkel(c1_6__bvfunc_4,k6_margrel1))
         => k8_bvfunc_1(c1_6__bvfunc_4,A,k5_valuat_1(c1_6__bvfunc_4,A)) = k19_bvfunc_1(c1_6__bvfunc_4) ) )
   => ! [B] : 
        ( ~ v1_xboole_0(B)
       => ! [C] : 
            ( m2_fraenkel(C,B,k6_margrel1,k1_fraenkel(B,k6_margrel1))
           => k8_bvfunc_1(B,C,k5_valuat_1(B,C)) = k19_bvfunc_1(B) ) ) ),
    introduced(definition,[new_symbol(c1_6__bvfunc_4),file(bvfunc_4,c1_6__bvfunc_4)]),
    [interesting(0.8),axiom,file(bvfunc_4,c1_6__bvfunc_4)]).

fof(dh_c2_6__bvfunc_4,definition,
    ( ( m2_fraenkel(c2_6__bvfunc_4,c1_6__bvfunc_4,k6_margrel1,k1_fraenkel(c1_6__bvfunc_4,k6_margrel1))
     => k8_bvfunc_1(c1_6__bvfunc_4,c2_6__bvfunc_4,k5_valuat_1(c1_6__bvfunc_4,c2_6__bvfunc_4)) = k19_bvfunc_1(c1_6__bvfunc_4) )
   => ! [A] : 
        ( m2_fraenkel(A,c1_6__bvfunc_4,k6_margrel1,k1_fraenkel(c1_6__bvfunc_4,k6_margrel1))
       => k8_bvfunc_1(c1_6__bvfunc_4,A,k5_valuat_1(c1_6__bvfunc_4,A)) = k19_bvfunc_1(c1_6__bvfunc_4) ) ),
    introduced(definition,[new_symbol(c2_6__bvfunc_4),file(bvfunc_4,c2_6__bvfunc_4)]),
    [interesting(0.8),axiom,file(bvfunc_4,c2_6__bvfunc_4)]).

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(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_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_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_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_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_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(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_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_4,assumption,(
    ~ v1_xboole_0(c1_6__bvfunc_4) ),
    introduced(assumption,[file(bvfunc_4,c1_6__bvfunc_4)]),
    [interesting(0.8),axiom,file(bvfunc_4,c1_6__bvfunc_4)]).

fof(dt_c2_6__bvfunc_4,assumption,(
    m2_fraenkel(c2_6__bvfunc_4,c1_6__bvfunc_4,k6_margrel1,k1_fraenkel(c1_6__bvfunc_4,k6_margrel1)) ),
    introduced(assumption,[file(bvfunc_4,c2_6__bvfunc_4)]),
    [interesting(0.8),axiom,file(bvfunc_4,c2_6__bvfunc_4)]).

fof(dh_c3_6__bvfunc_4,definition,
    ( ? [A] : 
        ( v1_relat_1(A)
        & v1_funct_1(A)
        & k8_bvfunc_1(c1_6__bvfunc_4,c2_6__bvfunc_4,k5_valuat_1(c1_6__bvfunc_4,c2_6__bvfunc_4)) = A
        & k1_relat_1(A) = c1_6__bvfunc_4
        & r1_tarski(k2_relat_1(A),k6_margrel1) )
   => ( v1_relat_1(c3_6__bvfunc_4)
      & v1_funct_1(c3_6__bvfunc_4)
      & k8_bvfunc_1(c1_6__bvfunc_4,c2_6__bvfunc_4,k5_valuat_1(c1_6__bvfunc_4,c2_6__bvfunc_4)) = c3_6__bvfunc_4
      & k1_relat_1(c3_6__bvfunc_4) = c1_6__bvfunc_4
      & r1_tarski(k2_relat_1(c3_6__bvfunc_4),k6_margrel1) ) ),
    introduced(definition,[new_symbol(c3_6__bvfunc_4),file(bvfunc_4,c3_6__bvfunc_4)]),
    [interesting(0.8),axiom,file(bvfunc_4,c3_6__bvfunc_4)]).

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_4,plain,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & k8_bvfunc_1(c1_6__bvfunc_4,c2_6__bvfunc_4,k5_valuat_1(c1_6__bvfunc_4,c2_6__bvfunc_4)) = A
      & k1_relat_1(A) = c1_6__bvfunc_4
      & r1_tarski(k2_relat_1(A),k6_margrel1) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6__bvfunc_4,dt_c2_6__bvfunc_4])],[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,rc1_valuat_1,rc2_margrel1,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_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_k8_bvfunc_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,redefinition_k5_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_k8_bvfunc_1,dt_c1_6__bvfunc_4,dt_c2_6__bvfunc_4,fc1_fraenkel,fc3_margrel1,t1_subset,t3_subset,t7_boole,d2_funct_2]),
    [interesting(0.8),file(bvfunc_4,e2_6__bvfunc_4),[file(bvfunc_4,e2_6__bvfunc_4)]]).

fof(dt_c3_6__bvfunc_4,plain,
    ( v1_relat_1(c3_6__bvfunc_4)
    & v1_funct_1(c3_6__bvfunc_4) ),
    inference(consider,[status(thm),assumptions([dt_c1_6__bvfunc_4,dt_c2_6__bvfunc_4])],[dh_c3_6__bvfunc_4,e2_6__bvfunc_4]),
    [interesting(0.8),file(bvfunc_4,c3_6__bvfunc_4),[file(bvfunc_4,c3_6__bvfunc_4)]]).

fof(dh_c4_6__bvfunc_4,definition,
    ( ? [A] : 
        ( v1_relat_1(A)
        & v1_funct_1(A)
        & k19_bvfunc_1(c1_6__bvfunc_4) = A
        & k1_relat_1(A) = c1_6__bvfunc_4
        & r1_tarski(k2_relat_1(A),k6_margrel1) )
   => ( v1_relat_1(c4_6__bvfunc_4)
      & v1_funct_1(c4_6__bvfunc_4)
      & k19_bvfunc_1(c1_6__bvfunc_4) = c4_6__bvfunc_4
      & k1_relat_1(c4_6__bvfunc_4) = c1_6__bvfunc_4
      & r1_tarski(k2_relat_1(c4_6__bvfunc_4),k6_margrel1) ) ),
    introduced(definition,[new_symbol(c4_6__bvfunc_4),file(bvfunc_4,c4_6__bvfunc_4)]),
    [interesting(0.8),axiom,file(bvfunc_4,c4_6__bvfunc_4)]).

fof(e4_6__bvfunc_4,plain,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & k19_bvfunc_1(c1_6__bvfunc_4) = A
      & k1_relat_1(A) = c1_6__bvfunc_4
      & r1_tarski(k2_relat_1(A),k6_margrel1) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6__bvfunc_4])],[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_k19_bvfunc_1,dt_k1_funct_2,dt_k1_relat_1,dt_k2_relat_1,dt_k6_margrel1,dt_c1_6__bvfunc_4,fc1_fraenkel,fc3_margrel1,t1_subset,t3_subset,t7_boole,d2_funct_2]),
    [interesting(0.8),file(bvfunc_4,e4_6__bvfunc_4),[file(bvfunc_4,e4_6__bvfunc_4)]]).

fof(dt_c4_6__bvfunc_4,plain,
    ( v1_relat_1(c4_6__bvfunc_4)
    & v1_funct_1(c4_6__bvfunc_4) ),
    inference(consider,[status(thm),assumptions([dt_c1_6__bvfunc_4])],[dh_c4_6__bvfunc_4,e4_6__bvfunc_4]),
    [interesting(0.8),file(bvfunc_4,c4_6__bvfunc_4),[file(bvfunc_4,c4_6__bvfunc_4)]]).

fof(dh_c1_6_1__bvfunc_4,definition,
    ( ( m1_subset_1(c1_6_1__bvfunc_4,c1_6__bvfunc_4)
     => k1_funct_1(k8_bvfunc_1(c1_6__bvfunc_4,c2_6__bvfunc_4,k5_valuat_1(c1_6__bvfunc_4,c2_6__bvfunc_4)),c1_6_1__bvfunc_4) = k1_funct_1(k19_bvfunc_1(c1_6__bvfunc_4),c1_6_1__bvfunc_4) )
   => ! [A] : 
        ( m1_subset_1(A,c1_6__bvfunc_4)
       => k1_funct_1(k8_bvfunc_1(c1_6__bvfunc_4,c2_6__bvfunc_4,k5_valuat_1(c1_6__bvfunc_4,c2_6__bvfunc_4)),A) = k1_funct_1(k19_bvfunc_1(c1_6__bvfunc_4),A) ) ),
    introduced(definition,[new_symbol(c1_6_1__bvfunc_4),file(bvfunc_4,c1_6_1__bvfunc_4)]),
    [interesting(0.65),axiom,file(bvfunc_4,c1_6_1__bvfunc_4)]).

fof(dt_k8_margrel1,axiom,(
    m1_subset_1(k8_margrel1,k6_margrel1) ),
    file(margrel1,k8_margrel1),
    [interesting(0.9),axiom,file(margrel1,k8_margrel1)]).

fof(dt_c1_6_1__bvfunc_4,assumption,(
    m1_subset_1(c1_6_1__bvfunc_4,c1_6__bvfunc_4) ),
    introduced(assumption,[file(bvfunc_4,c1_6_1__bvfunc_4)]),
    [interesting(0.65),axiom,file(bvfunc_4,c1_6_1__bvfunc_4)]).

fof(fc1_binarith,theorem,(
    ! [A,B] : 
      ( ( v2_margrel1(A)
        & v2_margrel1(B) )
     => v2_margrel1(k1_binarith(A,B)) ) ),
    file(binarith,fc1_binarith),
    [interesting(0.9),axiom,file(binarith,fc1_binarith)]).

fof(commutativity_k1_binarith,theorem,(
    ! [A,B] : 
      ( ( v2_margrel1(A)
        & v2_margrel1(B) )
     => k1_binarith(A,B) = k1_binarith(B,A) ) ),
    file(binarith,k1_binarith),
    [interesting(0.9),axiom,file(binarith,k1_binarith)]).

fof(commutativity_k3_binarith,theorem,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k6_margrel1)
        & m1_subset_1(B,k6_margrel1) )
     => k3_binarith(A,B) = k3_binarith(B,A) ) ),
    file(binarith,k3_binarith),
    [interesting(0.9),axiom,file(binarith,k3_binarith)]).

fof(redefinition_k3_binarith,definition,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k6_margrel1)
        & m1_subset_1(B,k6_margrel1) )
     => k3_binarith(A,B) = k1_binarith(A,B) ) ),
    file(binarith,k3_binarith),
    [interesting(0.9),axiom,file(binarith,k3_binarith)]).

fof(redefinition_k8_funct_2,definition,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B)
        & m1_subset_1(D,A) )
     => k8_funct_2(A,B,C,D) = k1_funct_1(C,D) ) ),
    file(funct_2,k8_funct_2),
    [interesting(0.9),axiom,file(funct_2,k8_funct_2)]).

fof(dt_k1_binarith,axiom,(
    $true ),
    file(binarith,k1_binarith),
    [interesting(0.9),axiom,file(binarith,k1_binarith)]).

fof(dt_k3_binarith,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k6_margrel1)
        & m1_subset_1(B,k6_margrel1) )
     => m1_subset_1(k3_binarith(A,B),k6_margrel1) ) ),
    file(binarith,k3_binarith),
    [interesting(0.9),axiom,file(binarith,k3_binarith)]).

fof(dt_k8_funct_2,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B)
        & m1_subset_1(D,A) )
     => m1_subset_1(k8_funct_2(A,B,C,D),B) ) ),
    file(funct_2,k8_funct_2),
    [interesting(0.9),axiom,file(funct_2,k8_funct_2)]).

fof(d7_bvfunc_1,definition,(
    ! [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))
                 => ( D = k8_bvfunc_1(A,B,C)
                  <=> ! [E] : 
                        ( m1_subset_1(E,A)
                       => k8_funct_2(A,k6_margrel1,D,E) = k3_binarith(k8_funct_2(A,k6_margrel1,B,E),k8_funct_2(A,k6_margrel1,C,E)) ) ) ) ) ) ) ),
    file(bvfunc_1,d7_bvfunc_1),
    [interesting(0.9),axiom,file(bvfunc_1,d7_bvfunc_1)]).

fof(e1_6_1_1__bvfunc_4,plain,(
    k1_funct_1(k8_bvfunc_1(c1_6__bvfunc_4,c2_6__bvfunc_4,k5_valuat_1(c1_6__bvfunc_4,c2_6__bvfunc_4)),c1_6_1__bvfunc_4) = k1_binarith(k1_funct_1(c2_6__bvfunc_4,c1_6_1__bvfunc_4),k1_funct_1(k5_valuat_1(c1_6__bvfunc_4,c2_6__bvfunc_4),c1_6_1__bvfunc_4)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6__bvfunc_4,dt_c1_6_1__bvfunc_4,dt_c2_6__bvfunc_4])],[reflexivity_r1_tarski,dt_k1_zfmisc_1,dt_k2_zfmisc_1,cc1_fraenkel,rc1_fraenkel,rc1_margrel1,t3_subset,t4_subset,t5_subset,commutativity_k6_bvfunc_1,antisymmetry_r2_hidden,existence_m1_fraenkel,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_funct_2,dt_k1_xboole_0,dt_k3_valuat_1,dt_k6_bvfunc_1,dt_m1_fraenkel,dt_m1_relset_1,dt_m2_relset_1,fc1_binarith,fc1_fraenkel,fc1_margrel1,fc2_valuat_1,fc3_valuat_1,rc1_valuat_1,rc2_margrel1,t1_subset,commutativity_k1_binarith,commutativity_k3_binarith,commutativity_k8_bvfunc_1,existence_m1_subset_1,existence_m2_fraenkel,redefinition_k1_fraenkel,redefinition_k3_binarith,redefinition_k5_valuat_1,redefinition_k8_bvfunc_1,redefinition_k8_funct_2,redefinition_m2_fraenkel,dt_k1_binarith,dt_k1_fraenkel,dt_k1_funct_1,dt_k3_binarith,dt_k5_valuat_1,dt_k6_margrel1,dt_k8_bvfunc_1,dt_k8_funct_2,dt_m1_subset_1,dt_m2_fraenkel,dt_c1_6__bvfunc_4,dt_c1_6_1__bvfunc_4,dt_c2_6__bvfunc_4,cc1_margrel1,cc1_valuat_1,fc3_margrel1,t2_subset,t6_boole,t7_boole,t8_boole,d7_bvfunc_1]),
    [interesting(0.5),file(bvfunc_4,e1_6_1_1__bvfunc_4),[file(bvfunc_4,e1_6_1_1__bvfunc_4)]]).

fof(fc4_margrel1,theorem,(
    ! [A] : 
      ( v2_margrel1(A)
     => v2_margrel1(k9_margrel1(A)) ) ),
    file(margrel1,fc4_margrel1),
    [interesting(0.9),axiom,file(margrel1,fc4_margrel1)]).

fof(involutiveness_k11_margrel1,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k6_margrel1)
     => k11_margrel1(k11_margrel1(A)) = A ) ),
    file(margrel1,k11_margrel1),
    [interesting(0.9),axiom,file(margrel1,k11_margrel1)]).

fof(involutiveness_k9_margrel1,theorem,(
    ! [A] : 
      ( v2_margrel1(A)
     => k9_margrel1(k9_margrel1(A)) = A ) ),
    file(margrel1,k9_margrel1),
    [interesting(0.9),axiom,file(margrel1,k9_margrel1)]).

fof(redefinition_k11_margrel1,definition,(
    ! [A] : 
      ( m1_subset_1(A,k6_margrel1)
     => k11_margrel1(A) = k9_margrel1(A) ) ),
    file(margrel1,k11_margrel1),
    [interesting(0.9),axiom,file(margrel1,k11_margrel1)]).

fof(dt_k11_margrel1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k6_margrel1)
     => m1_subset_1(k11_margrel1(A),k6_margrel1) ) ),
    file(margrel1,k11_margrel1),
    [interesting(0.9),axiom,file(margrel1,k11_margrel1)]).

fof(dt_k9_margrel1,axiom,(
    ! [A] : 
      ( v2_margrel1(A)
     => v2_margrel1(k9_margrel1(A)) ) ),
    file(margrel1,k9_margrel1),
    [interesting(0.9),axiom,file(margrel1,k9_margrel1)]).

fof(d5_valuat_1,definition,(
    ! [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))
             => ( C = k5_valuat_1(A,B)
              <=> ! [D] : 
                    ( m1_subset_1(D,A)
                   => k8_funct_2(A,k6_margrel1,C,D) = k11_margrel1(k8_funct_2(A,k6_margrel1,B,D)) ) ) ) ) ) ),
    file(valuat_1,d5_valuat_1),
    [interesting(0.9),axiom,file(valuat_1,d5_valuat_1)]).

fof(e2_6_1_1__bvfunc_4,plain,(
    k1_binarith(k1_funct_1(c2_6__bvfunc_4,c1_6_1__bvfunc_4),k1_funct_1(k5_valuat_1(c1_6__bvfunc_4,c2_6__bvfunc_4),c1_6_1__bvfunc_4)) = k1_binarith(k1_funct_1(c2_6__bvfunc_4,c1_6_1__bvfunc_4),k9_margrel1(k1_funct_1(c2_6__bvfunc_4,c1_6_1__bvfunc_4))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6__bvfunc_4,dt_c1_6_1__bvfunc_4,dt_c2_6__bvfunc_4])],[reflexivity_r1_tarski,dt_k1_zfmisc_1,dt_k2_zfmisc_1,cc1_fraenkel,rc1_fraenkel,rc1_margrel1,t3_subset,t4_subset,t5_subset,antisymmetry_r2_hidden,existence_m1_fraenkel,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_funct_2,dt_k1_xboole_0,dt_k3_valuat_1,dt_m1_fraenkel,dt_m1_relset_1,dt_m2_relset_1,fc1_binarith,fc1_fraenkel,fc1_margrel1,fc2_valuat_1,fc3_valuat_1,fc4_margrel1,rc1_valuat_1,rc2_margrel1,t1_subset,involutiveness_k11_margrel1,commutativity_k1_binarith,involutiveness_k9_margrel1,existence_m1_subset_1,existence_m2_fraenkel,redefinition_k11_margrel1,redefinition_k1_fraenkel,redefinition_k5_valuat_1,redefinition_k8_funct_2,redefinition_m2_fraenkel,dt_k11_margrel1,dt_k1_binarith,dt_k1_fraenkel,dt_k1_funct_1,dt_k5_valuat_1,dt_k6_margrel1,dt_k8_funct_2,dt_k9_margrel1,dt_m1_subset_1,dt_m2_fraenkel,dt_c1_6__bvfunc_4,dt_c1_6_1__bvfunc_4,dt_c2_6__bvfunc_4,cc1_margrel1,cc1_valuat_1,fc3_margrel1,t2_subset,t6_boole,t7_boole,t8_boole,d5_valuat_1]),
    [interesting(0.5),file(bvfunc_4,e2_6_1_1__bvfunc_4),[file(bvfunc_4,e2_6_1_1__bvfunc_4)]]).

fof(t18_binarith,theorem,(
    ! [A] : 
      ( v2_margrel1(A)
     => k1_binarith(A,k9_margrel1(A)) = k8_margrel1 ) ),
    file(binarith,t18_binarith),
    [interesting(0.9),axiom,file(binarith,t18_binarith)]).

fof(e3_6_1_1__bvfunc_4,plain,(
    k1_binarith(k1_funct_1(c2_6__bvfunc_4,c1_6_1__bvfunc_4),k9_margrel1(k1_funct_1(c2_6__bvfunc_4,c1_6_1__bvfunc_4))) = k8_margrel1 ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6__bvfunc_4,dt_c1_6_1__bvfunc_4,dt_c2_6__bvfunc_4])],[reflexivity_r1_tarski,rc1_margrel1,antisymmetry_r2_hidden,existence_m1_relset_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_fraenkel,fc1_margrel1,rc1_fraenkel,t1_subset,t3_subset,t4_subset,t5_subset,existence_m1_fraenkel,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_funct_2,dt_m1_fraenkel,dt_m2_relset_1,fc1_fraenkel,fc2_valuat_1,rc1_valuat_1,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_subset_1,existence_m2_fraenkel,redefinition_k1_fraenkel,redefinition_m2_fraenkel,dt_k1_fraenkel,dt_k6_margrel1,dt_m1_subset_1,dt_m2_fraenkel,dt_c1_6__bvfunc_4,cc1_margrel1,cc1_valuat_1,fc3_margrel1,commutativity_k1_binarith,involutiveness_k9_margrel1,dt_k1_binarith,dt_k1_funct_1,dt_k8_margrel1,dt_k9_margrel1,dt_c1_6_1__bvfunc_4,dt_c2_6__bvfunc_4,fc1_binarith,fc4_margrel1,rc2_margrel1,t18_binarith]),
    [interesting(0.5),file(bvfunc_4,e3_6_1_1__bvfunc_4),[file(bvfunc_4,e3_6_1_1__bvfunc_4)]]).

fof(e1_6_1__bvfunc_4,plain,(
    k1_funct_1(k8_bvfunc_1(c1_6__bvfunc_4,c2_6__bvfunc_4,k5_valuat_1(c1_6__bvfunc_4,c2_6__bvfunc_4)),c1_6_1__bvfunc_4) = k8_margrel1 ),
    inference(iterative_eq,[status(thm),assumptions([dt_c1_6__bvfunc_4,dt_c1_6_1__bvfunc_4,dt_c2_6__bvfunc_4])],[e1_6_1_1__bvfunc_4,e2_6_1_1__bvfunc_4,e3_6_1_1__bvfunc_4]),
    [interesting(0.65),file(bvfunc_4,e1_6_1__bvfunc_4),[file(bvfunc_4,e1_6_1__bvfunc_4)]]).

fof(d14_bvfunc_1,definition,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ( B = k19_bvfunc_1(A)
          <=> ! [C] : 
                ( m1_subset_1(C,A)
               => k1_funct_1(B,C) = k8_margrel1 ) ) ) ) ),
    file(bvfunc_1,d14_bvfunc_1),
    [interesting(0.9),axiom,file(bvfunc_1,d14_bvfunc_1)]).

fof(e2_6_1__bvfunc_4,plain,(
    k1_funct_1(k8_bvfunc_1(c1_6__bvfunc_4,c2_6__bvfunc_4,k5_valuat_1(c1_6__bvfunc_4,c2_6__bvfunc_4)),c1_6_1__bvfunc_4) = k1_funct_1(k19_bvfunc_1(c1_6__bvfunc_4),c1_6_1__bvfunc_4) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6__bvfunc_4,dt_c1_6_1__bvfunc_4,dt_c2_6__bvfunc_4])],[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,commutativity_k6_bvfunc_1,antisymmetry_r2_hidden,existence_m1_fraenkel,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_funct_2,dt_k1_xboole_0,dt_k3_valuat_1,dt_k6_bvfunc_1,dt_m1_fraenkel,dt_m2_relset_1,fc1_fraenkel,fc1_margrel1,fc2_valuat_1,fc3_valuat_1,rc1_valuat_1,rc2_margrel1,t1_subset,commutativity_k8_bvfunc_1,existence_m1_subset_1,existence_m2_fraenkel,redefinition_k1_fraenkel,redefinition_k5_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_k8_bvfunc_1,dt_k8_margrel1,dt_m1_subset_1,dt_m2_fraenkel,dt_c1_6__bvfunc_4,dt_c1_6_1__bvfunc_4,dt_c2_6__bvfunc_4,cc1_margrel1,cc1_valuat_1,fc3_margrel1,t2_subset,t6_boole,t7_boole,t8_boole,e1_6_1__bvfunc_4,d14_bvfunc_1]),
    [interesting(0.65),file(bvfunc_4,e2_6_1__bvfunc_4),[file(bvfunc_4,e2_6_1__bvfunc_4)]]).

fof(i2_6_1__bvfunc_4,theorem,(
    $true ),
    introduced(tautology,[file(bvfunc_4,i2_6_1__bvfunc_4)]),
    [interesting(0.65),trivial,file(bvfunc_4,i2_6_1__bvfunc_4)]).

fof(i1_6_1__bvfunc_4,plain,(
    k1_funct_1(k8_bvfunc_1(c1_6__bvfunc_4,c2_6__bvfunc_4,k5_valuat_1(c1_6__bvfunc_4,c2_6__bvfunc_4)),c1_6_1__bvfunc_4) = k1_funct_1(k19_bvfunc_1(c1_6__bvfunc_4),c1_6_1__bvfunc_4) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_6__bvfunc_4,dt_c1_6_1__bvfunc_4,dt_c2_6__bvfunc_4])],[e2_6_1__bvfunc_4,i2_6_1__bvfunc_4]),
    [interesting(0.65),file(bvfunc_4,i1_6_1__bvfunc_4),[file(bvfunc_4,i1_6_1__bvfunc_4)]]).

fof(i1_6_1_tmp__bvfunc_4,plain,
    ( m1_subset_1(c1_6_1__bvfunc_4,c1_6__bvfunc_4)
   => k1_funct_1(k8_bvfunc_1(c1_6__bvfunc_4,c2_6__bvfunc_4,k5_valuat_1(c1_6__bvfunc_4,c2_6__bvfunc_4)),c1_6_1__bvfunc_4) = k1_funct_1(k19_bvfunc_1(c1_6__bvfunc_4),c1_6_1__bvfunc_4) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_6__bvfunc_4,dt_c2_6__bvfunc_4]),discharge_asm(discharge,[dt_c1_6_1__bvfunc_4])],[dt_c1_6_1__bvfunc_4,i1_6_1__bvfunc_4]),
    [interesting(0.8),e1_6__bvfunc_4]).

fof(e1_6__bvfunc_4,plain,(
    ! [A] : 
      ( m1_subset_1(A,c1_6__bvfunc_4)
     => k1_funct_1(k8_bvfunc_1(c1_6__bvfunc_4,c2_6__bvfunc_4,k5_valuat_1(c1_6__bvfunc_4,c2_6__bvfunc_4)),A) = k1_funct_1(k19_bvfunc_1(c1_6__bvfunc_4),A) ) ),
    inference(let,[status(thm),assumptions([dt_c1_6__bvfunc_4,dt_c2_6__bvfunc_4])],[i1_6_1_tmp__bvfunc_4,dh_c1_6_1__bvfunc_4]),
    [interesting(0.8),file(bvfunc_4,e1_6__bvfunc_4),[file(bvfunc_4,e1_6__bvfunc_4)]]).

fof(e3_6__bvfunc_4,plain,
    ( k8_bvfunc_1(c1_6__bvfunc_4,c2_6__bvfunc_4,k5_valuat_1(c1_6__bvfunc_4,c2_6__bvfunc_4)) = c3_6__bvfunc_4
    & k1_relat_1(c3_6__bvfunc_4) = c1_6__bvfunc_4
    & r1_tarski(k2_relat_1(c3_6__bvfunc_4),k6_margrel1) ),
    inference(consider,[status(thm),assumptions([dt_c1_6__bvfunc_4,dt_c2_6__bvfunc_4])],[dh_c3_6__bvfunc_4,e2_6__bvfunc_4]),
    [interesting(0.8),file(bvfunc_4,e3_6__bvfunc_4),[file(bvfunc_4,e3_6__bvfunc_4)]]).

fof(e5_6__bvfunc_4,plain,
    ( k19_bvfunc_1(c1_6__bvfunc_4) = c4_6__bvfunc_4
    & k1_relat_1(c4_6__bvfunc_4) = c1_6__bvfunc_4
    & r1_tarski(k2_relat_1(c4_6__bvfunc_4),k6_margrel1) ),
    inference(consider,[status(thm),assumptions([dt_c1_6__bvfunc_4])],[dh_c4_6__bvfunc_4,e4_6__bvfunc_4]),
    [interesting(0.8),file(bvfunc_4,e5_6__bvfunc_4),[file(bvfunc_4,e5_6__bvfunc_4)]]).

fof(e6_6__bvfunc_4,plain,(
    ! [A] : 
      ( r2_hidden(A,c1_6__bvfunc_4)
     => k1_funct_1(c3_6__bvfunc_4,A) = k1_funct_1(c4_6__bvfunc_4,A) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_6__bvfunc_4,dt_c1_6__bvfunc_4])],[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,rc1_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_k6_bvfunc_1,dt_m2_fraenkel,cc1_valuat_1,rc2_margrel1,t2_subset,t4_subset,t5_subset,t6_boole,t8_boole,commutativity_k8_bvfunc_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_m1_subset_1,redefinition_k5_valuat_1,redefinition_k8_bvfunc_1,dt_k19_bvfunc_1,dt_k1_funct_1,dt_k1_relat_1,dt_k2_relat_1,dt_k5_valuat_1,dt_k6_margrel1,dt_k8_bvfunc_1,dt_m1_subset_1,dt_c1_6__bvfunc_4,dt_c2_6__bvfunc_4,dt_c3_6__bvfunc_4,dt_c4_6__bvfunc_4,cc1_margrel1,fc3_margrel1,t1_subset,t3_subset,t7_boole,e1_6__bvfunc_4,e3_6__bvfunc_4,e5_6__bvfunc_4]),
    [interesting(0.8),file(bvfunc_4,e6_6__bvfunc_4),[file(bvfunc_4,e6_6__bvfunc_4)]]).

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_4,plain,(
    k8_bvfunc_1(c1_6__bvfunc_4,c2_6__bvfunc_4,k5_valuat_1(c1_6__bvfunc_4,c2_6__bvfunc_4)) = k19_bvfunc_1(c1_6__bvfunc_4) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_6__bvfunc_4,dt_c1_6__bvfunc_4])],[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,rc1_valuat_1,rc2_margrel1,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_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_k8_bvfunc_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,redefinition_k5_valuat_1,redefinition_k8_bvfunc_1,dt_k19_bvfunc_1,dt_k1_funct_1,dt_k1_relat_1,dt_k2_relat_1,dt_k5_valuat_1,dt_k6_margrel1,dt_k8_bvfunc_1,dt_c1_6__bvfunc_4,dt_c2_6__bvfunc_4,dt_c3_6__bvfunc_4,dt_c4_6__bvfunc_4,fc3_margrel1,t1_subset,t3_subset,t7_boole,e6_6__bvfunc_4,e3_6__bvfunc_4,e5_6__bvfunc_4,t9_funct_1]),
    [interesting(0.8),file(bvfunc_4,e7_6__bvfunc_4),[file(bvfunc_4,e7_6__bvfunc_4)]]).

fof(i3_6__bvfunc_4,theorem,(
    $true ),
    introduced(tautology,[file(bvfunc_4,i3_6__bvfunc_4)]),
    [interesting(0.8),trivial,file(bvfunc_4,i3_6__bvfunc_4)]).

fof(i2_6__bvfunc_4,plain,(
    k8_bvfunc_1(c1_6__bvfunc_4,c2_6__bvfunc_4,k5_valuat_1(c1_6__bvfunc_4,c2_6__bvfunc_4)) = k19_bvfunc_1(c1_6__bvfunc_4) ),
    inference(conclusion,[status(thm),assumptions([dt_c2_6__bvfunc_4,dt_c1_6__bvfunc_4])],[e7_6__bvfunc_4,i3_6__bvfunc_4]),
    [interesting(0.8),file(bvfunc_4,i2_6__bvfunc_4),[file(bvfunc_4,i2_6__bvfunc_4)]]).

fof(i2_6_tmp__bvfunc_4,plain,
    ( m2_fraenkel(c2_6__bvfunc_4,c1_6__bvfunc_4,k6_margrel1,k1_fraenkel(c1_6__bvfunc_4,k6_margrel1))
   => k8_bvfunc_1(c1_6__bvfunc_4,c2_6__bvfunc_4,k5_valuat_1(c1_6__bvfunc_4,c2_6__bvfunc_4)) = k19_bvfunc_1(c1_6__bvfunc_4) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_6__bvfunc_4]),discharge_asm(discharge,[dt_c2_6__bvfunc_4])],[dt_c2_6__bvfunc_4,i2_6__bvfunc_4]),
    [interesting(0.8),i1_6__bvfunc_4]).

fof(i1_6__bvfunc_4,plain,(
    ! [A] : 
      ( m2_fraenkel(A,c1_6__bvfunc_4,k6_margrel1,k1_fraenkel(c1_6__bvfunc_4,k6_margrel1))
     => k8_bvfunc_1(c1_6__bvfunc_4,A,k5_valuat_1(c1_6__bvfunc_4,A)) = k19_bvfunc_1(c1_6__bvfunc_4) ) ),
    inference(let,[status(thm),assumptions([dt_c1_6__bvfunc_4])],[i2_6_tmp__bvfunc_4,dh_c2_6__bvfunc_4]),
    [interesting(0.8),file(bvfunc_4,i1_6__bvfunc_4),[file(bvfunc_4,i1_6__bvfunc_4)]]).

fof(i1_6_tmp__bvfunc_4,plain,
    ( ~ v1_xboole_0(c1_6__bvfunc_4)
   => ! [A] : 
        ( m2_fraenkel(A,c1_6__bvfunc_4,k6_margrel1,k1_fraenkel(c1_6__bvfunc_4,k6_margrel1))
       => k8_bvfunc_1(c1_6__bvfunc_4,A,k5_valuat_1(c1_6__bvfunc_4,A)) = k19_bvfunc_1(c1_6__bvfunc_4) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_6__bvfunc_4])],[dt_c1_6__bvfunc_4,i1_6__bvfunc_4]),
    [interesting(1),t6_bvfunc_4]).

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) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_6_tmp__bvfunc_4,dh_c1_6__bvfunc_4]),
    [interesting(1),file(bvfunc_4,t6_bvfunc_4),[file(bvfunc_4,t6_bvfunc_4)]]).