% Mizar ND problem: t9_bvfunc25,bvfunc25,112,51 
fof(dh_c1_9__bvfunc25,definition,
    ( ( ~ v1_xboole_0(c1_9__bvfunc25)
     => ! [A] : 
          ( m2_fraenkel(A,c1_9__bvfunc25,k6_margrel1,k1_fraenkel(c1_9__bvfunc25,k6_margrel1))
         => ! [B] : 
              ( m2_fraenkel(B,c1_9__bvfunc25,k6_margrel1,k1_fraenkel(c1_9__bvfunc25,k6_margrel1))
             => ! [C] : 
                  ( m2_fraenkel(C,c1_9__bvfunc25,k6_margrel1,k1_fraenkel(c1_9__bvfunc25,k6_margrel1))
                 => k14_bvfunc_1(c1_9__bvfunc25,A,k14_bvfunc_1(c1_9__bvfunc25,B,C)) = k14_bvfunc_1(c1_9__bvfunc25,k14_bvfunc_1(c1_9__bvfunc25,A,B),k14_bvfunc_1(c1_9__bvfunc25,A,C)) ) ) ) )
   => ! [D] : 
        ( ~ v1_xboole_0(D)
       => ! [E] : 
            ( m2_fraenkel(E,D,k6_margrel1,k1_fraenkel(D,k6_margrel1))
           => ! [F] : 
                ( m2_fraenkel(F,D,k6_margrel1,k1_fraenkel(D,k6_margrel1))
               => ! [G] : 
                    ( m2_fraenkel(G,D,k6_margrel1,k1_fraenkel(D,k6_margrel1))
                   => k14_bvfunc_1(D,E,k14_bvfunc_1(D,F,G)) = k14_bvfunc_1(D,k14_bvfunc_1(D,E,F),k14_bvfunc_1(D,E,G)) ) ) ) ) ),
    introduced(definition,[new_symbol(c1_9__bvfunc25),file(bvfunc25,c1_9__bvfunc25)]),
    [interesting(0.8),axiom,file(bvfunc25,c1_9__bvfunc25)]).

fof(dh_c2_9__bvfunc25,definition,
    ( ( m2_fraenkel(c2_9__bvfunc25,c1_9__bvfunc25,k6_margrel1,k1_fraenkel(c1_9__bvfunc25,k6_margrel1))
     => ! [A] : 
          ( m2_fraenkel(A,c1_9__bvfunc25,k6_margrel1,k1_fraenkel(c1_9__bvfunc25,k6_margrel1))
         => ! [B] : 
              ( m2_fraenkel(B,c1_9__bvfunc25,k6_margrel1,k1_fraenkel(c1_9__bvfunc25,k6_margrel1))
             => k14_bvfunc_1(c1_9__bvfunc25,c2_9__bvfunc25,k14_bvfunc_1(c1_9__bvfunc25,A,B)) = k14_bvfunc_1(c1_9__bvfunc25,k14_bvfunc_1(c1_9__bvfunc25,c2_9__bvfunc25,A),k14_bvfunc_1(c1_9__bvfunc25,c2_9__bvfunc25,B)) ) ) )
   => ! [C] : 
        ( m2_fraenkel(C,c1_9__bvfunc25,k6_margrel1,k1_fraenkel(c1_9__bvfunc25,k6_margrel1))
       => ! [D] : 
            ( m2_fraenkel(D,c1_9__bvfunc25,k6_margrel1,k1_fraenkel(c1_9__bvfunc25,k6_margrel1))
           => ! [E] : 
                ( m2_fraenkel(E,c1_9__bvfunc25,k6_margrel1,k1_fraenkel(c1_9__bvfunc25,k6_margrel1))
               => k14_bvfunc_1(c1_9__bvfunc25,C,k14_bvfunc_1(c1_9__bvfunc25,D,E)) = k14_bvfunc_1(c1_9__bvfunc25,k14_bvfunc_1(c1_9__bvfunc25,C,D),k14_bvfunc_1(c1_9__bvfunc25,C,E)) ) ) ) ),
    introduced(definition,[new_symbol(c2_9__bvfunc25),file(bvfunc25,c2_9__bvfunc25)]),
    [interesting(0.8),axiom,file(bvfunc25,c2_9__bvfunc25)]).

fof(dh_c3_9__bvfunc25,definition,
    ( ( m2_fraenkel(c3_9__bvfunc25,c1_9__bvfunc25,k6_margrel1,k1_fraenkel(c1_9__bvfunc25,k6_margrel1))
     => ! [A] : 
          ( m2_fraenkel(A,c1_9__bvfunc25,k6_margrel1,k1_fraenkel(c1_9__bvfunc25,k6_margrel1))
         => k14_bvfunc_1(c1_9__bvfunc25,c2_9__bvfunc25,k14_bvfunc_1(c1_9__bvfunc25,c3_9__bvfunc25,A)) = k14_bvfunc_1(c1_9__bvfunc25,k14_bvfunc_1(c1_9__bvfunc25,c2_9__bvfunc25,c3_9__bvfunc25),k14_bvfunc_1(c1_9__bvfunc25,c2_9__bvfunc25,A)) ) )
   => ! [B] : 
        ( m2_fraenkel(B,c1_9__bvfunc25,k6_margrel1,k1_fraenkel(c1_9__bvfunc25,k6_margrel1))
       => ! [C] : 
            ( m2_fraenkel(C,c1_9__bvfunc25,k6_margrel1,k1_fraenkel(c1_9__bvfunc25,k6_margrel1))
           => k14_bvfunc_1(c1_9__bvfunc25,c2_9__bvfunc25,k14_bvfunc_1(c1_9__bvfunc25,B,C)) = k14_bvfunc_1(c1_9__bvfunc25,k14_bvfunc_1(c1_9__bvfunc25,c2_9__bvfunc25,B),k14_bvfunc_1(c1_9__bvfunc25,c2_9__bvfunc25,C)) ) ) ),
    introduced(definition,[new_symbol(c3_9__bvfunc25),file(bvfunc25,c3_9__bvfunc25)]),
    [interesting(0.8),axiom,file(bvfunc25,c3_9__bvfunc25)]).

fof(dh_c4_9__bvfunc25,definition,
    ( ( m2_fraenkel(c4_9__bvfunc25,c1_9__bvfunc25,k6_margrel1,k1_fraenkel(c1_9__bvfunc25,k6_margrel1))
     => k14_bvfunc_1(c1_9__bvfunc25,c2_9__bvfunc25,k14_bvfunc_1(c1_9__bvfunc25,c3_9__bvfunc25,c4_9__bvfunc25)) = k14_bvfunc_1(c1_9__bvfunc25,k14_bvfunc_1(c1_9__bvfunc25,c2_9__bvfunc25,c3_9__bvfunc25),k14_bvfunc_1(c1_9__bvfunc25,c2_9__bvfunc25,c4_9__bvfunc25)) )
   => ! [A] : 
        ( m2_fraenkel(A,c1_9__bvfunc25,k6_margrel1,k1_fraenkel(c1_9__bvfunc25,k6_margrel1))
       => k14_bvfunc_1(c1_9__bvfunc25,c2_9__bvfunc25,k14_bvfunc_1(c1_9__bvfunc25,c3_9__bvfunc25,A)) = k14_bvfunc_1(c1_9__bvfunc25,k14_bvfunc_1(c1_9__bvfunc25,c2_9__bvfunc25,c3_9__bvfunc25),k14_bvfunc_1(c1_9__bvfunc25,c2_9__bvfunc25,A)) ) ),
    introduced(definition,[new_symbol(c4_9__bvfunc25),file(bvfunc25,c4_9__bvfunc25)]),
    [interesting(0.8),axiom,file(bvfunc25,c4_9__bvfunc25)]).

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_k1_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k1_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,k1_zfmisc_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(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_fraenkel,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_fraenkel(A) ) ),
    file(fraenkel,rc1_fraenkel),
    [interesting(0.9),axiom,file(fraenkel,rc1_fraenkel)]).

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

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_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_k12_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(k12_bvfunc_1(A,B))
        & v1_funct_1(k12_bvfunc_1(A,B)) ) ) ),
    file(bvfunc_1,k12_bvfunc_1),
    [interesting(0.9),axiom,file(bvfunc_1,k12_bvfunc_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_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_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_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    [interesting(0.9),axiom,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),
    [interesting(0.9),axiom,file(relset_1,m2_relset_1)]).

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(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(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(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_k14_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)) )
     => k14_bvfunc_1(A,B,C) = k12_bvfunc_1(B,C) ) ),
    file(bvfunc_1,k14_bvfunc_1),
    [interesting(0.9),axiom,file(bvfunc_1,k14_bvfunc_1)]).

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_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(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_k14_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(k14_bvfunc_1(A,B,C),A,k6_margrel1,k1_fraenkel(A,k6_margrel1)) ) ),
    file(bvfunc_1,k14_bvfunc_1),
    [interesting(0.9),axiom,file(bvfunc_1,k14_bvfunc_1)]).

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_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_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(dt_c1_9__bvfunc25,assumption,(
    ~ v1_xboole_0(c1_9__bvfunc25) ),
    introduced(assumption,[file(bvfunc25,c1_9__bvfunc25)]),
    [interesting(0.8),axiom,file(bvfunc25,c1_9__bvfunc25)]).

fof(dt_c2_9__bvfunc25,assumption,(
    m2_fraenkel(c2_9__bvfunc25,c1_9__bvfunc25,k6_margrel1,k1_fraenkel(c1_9__bvfunc25,k6_margrel1)) ),
    introduced(assumption,[file(bvfunc25,c2_9__bvfunc25)]),
    [interesting(0.8),axiom,file(bvfunc25,c2_9__bvfunc25)]).

fof(dt_c3_9__bvfunc25,assumption,(
    m2_fraenkel(c3_9__bvfunc25,c1_9__bvfunc25,k6_margrel1,k1_fraenkel(c1_9__bvfunc25,k6_margrel1)) ),
    introduced(assumption,[file(bvfunc25,c3_9__bvfunc25)]),
    [interesting(0.8),axiom,file(bvfunc25,c3_9__bvfunc25)]).

fof(dt_c4_9__bvfunc25,assumption,(
    m2_fraenkel(c4_9__bvfunc25,c1_9__bvfunc25,k6_margrel1,k1_fraenkel(c1_9__bvfunc25,k6_margrel1)) ),
    introduced(assumption,[file(bvfunc25,c4_9__bvfunc25)]),
    [interesting(0.8),axiom,file(bvfunc25,c4_9__bvfunc25)]).

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

fof(t8_bvfunc_4,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))
             => k14_bvfunc_1(A,B,C) = k8_bvfunc_1(A,k5_valuat_1(A,B),C) ) ) ) ),
    file(bvfunc_4,t8_bvfunc_4),
    [interesting(0.9),axiom,file(bvfunc_4,t8_bvfunc_4)]).

fof(e1_9_1__bvfunc25,plain,(
    k14_bvfunc_1(c1_9__bvfunc25,k14_bvfunc_1(c1_9__bvfunc25,c2_9__bvfunc25,c3_9__bvfunc25),k14_bvfunc_1(c1_9__bvfunc25,c2_9__bvfunc25,c4_9__bvfunc25)) = k14_bvfunc_1(c1_9__bvfunc25,k14_bvfunc_1(c1_9__bvfunc25,c2_9__bvfunc25,c3_9__bvfunc25),k8_bvfunc_1(c1_9__bvfunc25,k5_valuat_1(c1_9__bvfunc25,c2_9__bvfunc25),c4_9__bvfunc25)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_9__bvfunc25,dt_c2_9__bvfunc25,dt_c3_9__bvfunc25,dt_c4_9__bvfunc25])],[existence_m1_relset_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_fraenkel,fc3_valuat_1,rc1_fraenkel,rc1_valuat_1,rc2_margrel1,commutativity_k6_bvfunc_1,existence_m1_fraenkel,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k12_bvfunc_1,dt_k1_funct_2,dt_k3_valuat_1,dt_k6_bvfunc_1,dt_m1_fraenkel,dt_m1_subset_1,dt_m2_relset_1,cc1_margrel1,cc1_valuat_1,fc1_fraenkel,commutativity_k8_bvfunc_1,existence_m2_fraenkel,redefinition_k14_bvfunc_1,redefinition_k1_fraenkel,redefinition_k5_valuat_1,redefinition_k8_bvfunc_1,redefinition_m2_fraenkel,dt_k14_bvfunc_1,dt_k1_fraenkel,dt_k5_valuat_1,dt_k6_margrel1,dt_k8_bvfunc_1,dt_m2_fraenkel,dt_c1_9__bvfunc25,dt_c2_9__bvfunc25,dt_c3_9__bvfunc25,dt_c4_9__bvfunc25,fc3_margrel1,t8_bvfunc_4]),
    [interesting(0.65),file(bvfunc25,e1_9_1__bvfunc25),[file(bvfunc25,e1_9_1__bvfunc25)]]).

fof(e2_9_1__bvfunc25,plain,(
    k14_bvfunc_1(c1_9__bvfunc25,k14_bvfunc_1(c1_9__bvfunc25,c2_9__bvfunc25,c3_9__bvfunc25),k8_bvfunc_1(c1_9__bvfunc25,k5_valuat_1(c1_9__bvfunc25,c2_9__bvfunc25),c4_9__bvfunc25)) = k8_bvfunc_1(c1_9__bvfunc25,k5_valuat_1(c1_9__bvfunc25,k14_bvfunc_1(c1_9__bvfunc25,c2_9__bvfunc25,c3_9__bvfunc25)),k8_bvfunc_1(c1_9__bvfunc25,k5_valuat_1(c1_9__bvfunc25,c2_9__bvfunc25),c4_9__bvfunc25)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_9__bvfunc25,dt_c2_9__bvfunc25,dt_c3_9__bvfunc25,dt_c4_9__bvfunc25])],[existence_m1_relset_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_fraenkel,fc3_valuat_1,rc1_fraenkel,rc1_valuat_1,rc2_margrel1,commutativity_k6_bvfunc_1,existence_m1_fraenkel,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k12_bvfunc_1,dt_k1_funct_2,dt_k3_valuat_1,dt_k6_bvfunc_1,dt_m1_fraenkel,dt_m1_subset_1,dt_m2_relset_1,cc1_margrel1,cc1_valuat_1,fc1_fraenkel,commutativity_k8_bvfunc_1,existence_m2_fraenkel,redefinition_k14_bvfunc_1,redefinition_k1_fraenkel,redefinition_k5_valuat_1,redefinition_k8_bvfunc_1,redefinition_m2_fraenkel,dt_k14_bvfunc_1,dt_k1_fraenkel,dt_k5_valuat_1,dt_k6_margrel1,dt_k8_bvfunc_1,dt_m2_fraenkel,dt_c1_9__bvfunc25,dt_c2_9__bvfunc25,dt_c3_9__bvfunc25,dt_c4_9__bvfunc25,fc3_margrel1,t8_bvfunc_4]),
    [interesting(0.65),file(bvfunc25,e2_9_1__bvfunc25),[file(bvfunc25,e2_9_1__bvfunc25)]]).

fof(e3_9_1__bvfunc25,plain,(
    k8_bvfunc_1(c1_9__bvfunc25,k5_valuat_1(c1_9__bvfunc25,k14_bvfunc_1(c1_9__bvfunc25,c2_9__bvfunc25,c3_9__bvfunc25)),k8_bvfunc_1(c1_9__bvfunc25,k5_valuat_1(c1_9__bvfunc25,c2_9__bvfunc25),c4_9__bvfunc25)) = k8_bvfunc_1(c1_9__bvfunc25,k5_valuat_1(c1_9__bvfunc25,k8_bvfunc_1(c1_9__bvfunc25,k5_valuat_1(c1_9__bvfunc25,c2_9__bvfunc25),c3_9__bvfunc25)),k8_bvfunc_1(c1_9__bvfunc25,k5_valuat_1(c1_9__bvfunc25,c2_9__bvfunc25),c4_9__bvfunc25)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_9__bvfunc25,dt_c2_9__bvfunc25,dt_c3_9__bvfunc25,dt_c4_9__bvfunc25])],[existence_m1_relset_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_fraenkel,fc3_valuat_1,rc1_fraenkel,rc1_valuat_1,rc2_margrel1,commutativity_k6_bvfunc_1,existence_m1_fraenkel,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k12_bvfunc_1,dt_k1_funct_2,dt_k3_valuat_1,dt_k6_bvfunc_1,dt_m1_fraenkel,dt_m1_subset_1,dt_m2_relset_1,cc1_margrel1,cc1_valuat_1,fc1_fraenkel,commutativity_k8_bvfunc_1,existence_m2_fraenkel,redefinition_k14_bvfunc_1,redefinition_k1_fraenkel,redefinition_k5_valuat_1,redefinition_k8_bvfunc_1,redefinition_m2_fraenkel,dt_k14_bvfunc_1,dt_k1_fraenkel,dt_k5_valuat_1,dt_k6_margrel1,dt_k8_bvfunc_1,dt_m2_fraenkel,dt_c1_9__bvfunc25,dt_c2_9__bvfunc25,dt_c3_9__bvfunc25,dt_c4_9__bvfunc25,fc3_margrel1,t8_bvfunc_4]),
    [interesting(0.65),file(bvfunc25,e3_9_1__bvfunc25),[file(bvfunc25,e3_9_1__bvfunc25)]]).

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(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(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(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(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(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(t16_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))
             => k5_valuat_1(A,k8_bvfunc_1(A,B,C)) = k6_valuat_1(A,k5_valuat_1(A,B),k5_valuat_1(A,C)) ) ) ) ),
    file(bvfunc_1,t16_bvfunc_1),
    [interesting(0.9),axiom,file(bvfunc_1,t16_bvfunc_1)]).

fof(e4_9_1__bvfunc25,plain,(
    k8_bvfunc_1(c1_9__bvfunc25,k5_valuat_1(c1_9__bvfunc25,k8_bvfunc_1(c1_9__bvfunc25,k5_valuat_1(c1_9__bvfunc25,c2_9__bvfunc25),c3_9__bvfunc25)),k8_bvfunc_1(c1_9__bvfunc25,k5_valuat_1(c1_9__bvfunc25,c2_9__bvfunc25),c4_9__bvfunc25)) = k8_bvfunc_1(c1_9__bvfunc25,k6_valuat_1(c1_9__bvfunc25,k5_valuat_1(c1_9__bvfunc25,k5_valuat_1(c1_9__bvfunc25,c2_9__bvfunc25)),k5_valuat_1(c1_9__bvfunc25,c3_9__bvfunc25)),k8_bvfunc_1(c1_9__bvfunc25,k5_valuat_1(c1_9__bvfunc25,c2_9__bvfunc25),c4_9__bvfunc25)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_9__bvfunc25,dt_c2_9__bvfunc25,dt_c3_9__bvfunc25,dt_c4_9__bvfunc25])],[existence_m1_relset_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_fraenkel,fc3_valuat_1,fc4_valuat_1,rc1_fraenkel,rc1_valuat_1,rc2_margrel1,commutativity_k4_valuat_1,commutativity_k6_bvfunc_1,existence_m1_fraenkel,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_funct_2,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,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_k5_valuat_1,dt_k6_margrel1,dt_k6_valuat_1,dt_k8_bvfunc_1,dt_m2_fraenkel,dt_c1_9__bvfunc25,dt_c2_9__bvfunc25,dt_c3_9__bvfunc25,dt_c4_9__bvfunc25,fc3_margrel1,t16_bvfunc_1]),
    [interesting(0.65),file(bvfunc25,e4_9_1__bvfunc25),[file(bvfunc25,e4_9_1__bvfunc25)]]).

fof(t4_bvfunc_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_valuat_1(A) )
     => k3_valuat_1(k3_valuat_1(A)) = A ) ),
    file(bvfunc_1,t4_bvfunc_1),
    [interesting(0.9),axiom,file(bvfunc_1,t4_bvfunc_1)]).

fof(e5_9_1__bvfunc25,plain,(
    k8_bvfunc_1(c1_9__bvfunc25,k6_valuat_1(c1_9__bvfunc25,k5_valuat_1(c1_9__bvfunc25,k5_valuat_1(c1_9__bvfunc25,c2_9__bvfunc25)),k5_valuat_1(c1_9__bvfunc25,c3_9__bvfunc25)),k8_bvfunc_1(c1_9__bvfunc25,k5_valuat_1(c1_9__bvfunc25,c2_9__bvfunc25),c4_9__bvfunc25)) = k8_bvfunc_1(c1_9__bvfunc25,k6_valuat_1(c1_9__bvfunc25,c2_9__bvfunc25,k5_valuat_1(c1_9__bvfunc25,c3_9__bvfunc25)),k8_bvfunc_1(c1_9__bvfunc25,k5_valuat_1(c1_9__bvfunc25,c2_9__bvfunc25),c4_9__bvfunc25)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_9__bvfunc25,dt_c2_9__bvfunc25,dt_c3_9__bvfunc25,dt_c4_9__bvfunc25])],[existence_m1_relset_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_fraenkel,rc1_fraenkel,existence_m1_fraenkel,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_funct_2,dt_m1_fraenkel,dt_m2_relset_1,fc1_fraenkel,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_k4_valuat_1,dt_k6_bvfunc_1,dt_k6_margrel1,dt_m1_subset_1,dt_m2_fraenkel,cc1_margrel1,cc1_valuat_1,fc3_margrel1,fc4_valuat_1,commutativity_k6_valuat_1,commutativity_k8_bvfunc_1,redefinition_k5_valuat_1,redefinition_k6_valuat_1,redefinition_k8_bvfunc_1,dt_k3_valuat_1,dt_k5_valuat_1,dt_k6_valuat_1,dt_k8_bvfunc_1,dt_c1_9__bvfunc25,dt_c2_9__bvfunc25,dt_c3_9__bvfunc25,dt_c4_9__bvfunc25,fc3_valuat_1,rc1_valuat_1,t4_bvfunc_1]),
    [interesting(0.65),file(bvfunc25,e5_9_1__bvfunc25),[file(bvfunc25,e5_9_1__bvfunc25)]]).

fof(t11_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))
                 => k8_bvfunc_1(A,k8_bvfunc_1(A,B,C),D) = k8_bvfunc_1(A,B,k8_bvfunc_1(A,C,D)) ) ) ) ) ),
    file(bvfunc_1,t11_bvfunc_1),
    [interesting(0.9),axiom,file(bvfunc_1,t11_bvfunc_1)]).

fof(e6_9_1__bvfunc25,plain,(
    k8_bvfunc_1(c1_9__bvfunc25,k6_valuat_1(c1_9__bvfunc25,c2_9__bvfunc25,k5_valuat_1(c1_9__bvfunc25,c3_9__bvfunc25)),k8_bvfunc_1(c1_9__bvfunc25,k5_valuat_1(c1_9__bvfunc25,c2_9__bvfunc25),c4_9__bvfunc25)) = k8_bvfunc_1(c1_9__bvfunc25,k8_bvfunc_1(c1_9__bvfunc25,k6_valuat_1(c1_9__bvfunc25,c2_9__bvfunc25,k5_valuat_1(c1_9__bvfunc25,c3_9__bvfunc25)),k5_valuat_1(c1_9__bvfunc25,c2_9__bvfunc25)),c4_9__bvfunc25) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_9__bvfunc25,dt_c2_9__bvfunc25,dt_c3_9__bvfunc25,dt_c4_9__bvfunc25])],[existence_m1_relset_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_fraenkel,fc3_valuat_1,fc4_valuat_1,rc1_fraenkel,rc1_valuat_1,rc2_margrel1,commutativity_k4_valuat_1,commutativity_k6_bvfunc_1,existence_m1_fraenkel,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_funct_2,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,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_k5_valuat_1,dt_k6_margrel1,dt_k6_valuat_1,dt_k8_bvfunc_1,dt_m2_fraenkel,dt_c1_9__bvfunc25,dt_c2_9__bvfunc25,dt_c3_9__bvfunc25,dt_c4_9__bvfunc25,fc3_margrel1,t11_bvfunc_1]),
    [interesting(0.65),file(bvfunc25,e6_9_1__bvfunc25),[file(bvfunc25,e6_9_1__bvfunc25)]]).

fof(t14_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))
                 => k8_bvfunc_1(A,k6_valuat_1(A,B,C),D) = k6_valuat_1(A,k8_bvfunc_1(A,B,D),k8_bvfunc_1(A,C,D)) ) ) ) ) ),
    file(bvfunc_1,t14_bvfunc_1),
    [interesting(0.9),axiom,file(bvfunc_1,t14_bvfunc_1)]).

fof(e7_9_1__bvfunc25,plain,(
    k8_bvfunc_1(c1_9__bvfunc25,k8_bvfunc_1(c1_9__bvfunc25,k6_valuat_1(c1_9__bvfunc25,c2_9__bvfunc25,k5_valuat_1(c1_9__bvfunc25,c3_9__bvfunc25)),k5_valuat_1(c1_9__bvfunc25,c2_9__bvfunc25)),c4_9__bvfunc25) = k8_bvfunc_1(c1_9__bvfunc25,k6_valuat_1(c1_9__bvfunc25,k8_bvfunc_1(c1_9__bvfunc25,c2_9__bvfunc25,k5_valuat_1(c1_9__bvfunc25,c2_9__bvfunc25)),k8_bvfunc_1(c1_9__bvfunc25,k5_valuat_1(c1_9__bvfunc25,c3_9__bvfunc25),k5_valuat_1(c1_9__bvfunc25,c2_9__bvfunc25))),c4_9__bvfunc25) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_9__bvfunc25,dt_c2_9__bvfunc25,dt_c3_9__bvfunc25,dt_c4_9__bvfunc25])],[existence_m1_relset_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_fraenkel,fc3_valuat_1,fc4_valuat_1,rc1_fraenkel,rc1_valuat_1,rc2_margrel1,commutativity_k4_valuat_1,commutativity_k6_bvfunc_1,existence_m1_fraenkel,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_funct_2,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,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_k5_valuat_1,dt_k6_margrel1,dt_k6_valuat_1,dt_k8_bvfunc_1,dt_m2_fraenkel,dt_c1_9__bvfunc25,dt_c2_9__bvfunc25,dt_c3_9__bvfunc25,dt_c4_9__bvfunc25,fc3_margrel1,t14_bvfunc_1]),
    [interesting(0.65),file(bvfunc25,e7_9_1__bvfunc25),[file(bvfunc25,e7_9_1__bvfunc25)]]).

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(e8_9_1__bvfunc25,plain,(
    k8_bvfunc_1(c1_9__bvfunc25,k6_valuat_1(c1_9__bvfunc25,k8_bvfunc_1(c1_9__bvfunc25,c2_9__bvfunc25,k5_valuat_1(c1_9__bvfunc25,c2_9__bvfunc25)),k8_bvfunc_1(c1_9__bvfunc25,k5_valuat_1(c1_9__bvfunc25,c3_9__bvfunc25),k5_valuat_1(c1_9__bvfunc25,c2_9__bvfunc25))),c4_9__bvfunc25) = k8_bvfunc_1(c1_9__bvfunc25,k6_valuat_1(c1_9__bvfunc25,k19_bvfunc_1(c1_9__bvfunc25),k8_bvfunc_1(c1_9__bvfunc25,k5_valuat_1(c1_9__bvfunc25,c3_9__bvfunc25),k5_valuat_1(c1_9__bvfunc25,c2_9__bvfunc25))),c4_9__bvfunc25) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_9__bvfunc25,dt_c2_9__bvfunc25,dt_c3_9__bvfunc25,dt_c4_9__bvfunc25])],[existence_m1_relset_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_fraenkel,fc3_valuat_1,fc4_valuat_1,rc1_fraenkel,rc1_valuat_1,rc2_margrel1,commutativity_k4_valuat_1,commutativity_k6_bvfunc_1,existence_m1_fraenkel,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_funct_2,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,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_k5_valuat_1,dt_k6_margrel1,dt_k6_valuat_1,dt_k8_bvfunc_1,dt_m2_fraenkel,dt_c1_9__bvfunc25,dt_c2_9__bvfunc25,dt_c3_9__bvfunc25,dt_c4_9__bvfunc25,fc3_margrel1,t6_bvfunc_4]),
    [interesting(0.65),file(bvfunc25,e8_9_1__bvfunc25),[file(bvfunc25,e8_9_1__bvfunc25)]]).

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(e9_9_1__bvfunc25,plain,(
    k8_bvfunc_1(c1_9__bvfunc25,k6_valuat_1(c1_9__bvfunc25,k19_bvfunc_1(c1_9__bvfunc25),k8_bvfunc_1(c1_9__bvfunc25,k5_valuat_1(c1_9__bvfunc25,c3_9__bvfunc25),k5_valuat_1(c1_9__bvfunc25,c2_9__bvfunc25))),c4_9__bvfunc25) = k8_bvfunc_1(c1_9__bvfunc25,k8_bvfunc_1(c1_9__bvfunc25,k5_valuat_1(c1_9__bvfunc25,c2_9__bvfunc25),k5_valuat_1(c1_9__bvfunc25,c3_9__bvfunc25)),c4_9__bvfunc25) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_9__bvfunc25,dt_c2_9__bvfunc25,dt_c3_9__bvfunc25,dt_c4_9__bvfunc25])],[existence_m1_relset_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_fraenkel,fc3_valuat_1,fc4_valuat_1,rc1_fraenkel,rc1_valuat_1,rc2_margrel1,commutativity_k4_valuat_1,commutativity_k6_bvfunc_1,existence_m1_fraenkel,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_funct_2,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,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_k5_valuat_1,dt_k6_margrel1,dt_k6_valuat_1,dt_k8_bvfunc_1,dt_m2_fraenkel,dt_c1_9__bvfunc25,dt_c2_9__bvfunc25,dt_c3_9__bvfunc25,dt_c4_9__bvfunc25,fc3_margrel1,t9_bvfunc_1]),
    [interesting(0.65),file(bvfunc25,e9_9_1__bvfunc25),[file(bvfunc25,e9_9_1__bvfunc25)]]).

fof(e10_9_1__bvfunc25,plain,(
    k8_bvfunc_1(c1_9__bvfunc25,k8_bvfunc_1(c1_9__bvfunc25,k5_valuat_1(c1_9__bvfunc25,c2_9__bvfunc25),k5_valuat_1(c1_9__bvfunc25,c3_9__bvfunc25)),c4_9__bvfunc25) = k8_bvfunc_1(c1_9__bvfunc25,k5_valuat_1(c1_9__bvfunc25,c2_9__bvfunc25),k8_bvfunc_1(c1_9__bvfunc25,k5_valuat_1(c1_9__bvfunc25,c3_9__bvfunc25),c4_9__bvfunc25)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_9__bvfunc25,dt_c2_9__bvfunc25,dt_c3_9__bvfunc25,dt_c4_9__bvfunc25])],[existence_m1_relset_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_fraenkel,fc3_valuat_1,rc1_fraenkel,rc1_valuat_1,rc2_margrel1,commutativity_k6_bvfunc_1,existence_m1_fraenkel,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_funct_2,dt_k3_valuat_1,dt_k6_bvfunc_1,dt_m1_fraenkel,dt_m1_subset_1,dt_m2_relset_1,cc1_margrel1,cc1_valuat_1,fc1_fraenkel,commutativity_k8_bvfunc_1,existence_m2_fraenkel,redefinition_k1_fraenkel,redefinition_k5_valuat_1,redefinition_k8_bvfunc_1,redefinition_m2_fraenkel,dt_k1_fraenkel,dt_k5_valuat_1,dt_k6_margrel1,dt_k8_bvfunc_1,dt_m2_fraenkel,dt_c1_9__bvfunc25,dt_c2_9__bvfunc25,dt_c3_9__bvfunc25,dt_c4_9__bvfunc25,fc3_margrel1,t11_bvfunc_1]),
    [interesting(0.65),file(bvfunc25,e10_9_1__bvfunc25),[file(bvfunc25,e10_9_1__bvfunc25)]]).

fof(e11_9_1__bvfunc25,plain,(
    k8_bvfunc_1(c1_9__bvfunc25,k5_valuat_1(c1_9__bvfunc25,c2_9__bvfunc25),k8_bvfunc_1(c1_9__bvfunc25,k5_valuat_1(c1_9__bvfunc25,c3_9__bvfunc25),c4_9__bvfunc25)) = k8_bvfunc_1(c1_9__bvfunc25,k5_valuat_1(c1_9__bvfunc25,c2_9__bvfunc25),k14_bvfunc_1(c1_9__bvfunc25,c3_9__bvfunc25,c4_9__bvfunc25)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_9__bvfunc25,dt_c2_9__bvfunc25,dt_c3_9__bvfunc25,dt_c4_9__bvfunc25])],[existence_m1_relset_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_fraenkel,fc3_valuat_1,rc1_fraenkel,rc1_valuat_1,rc2_margrel1,commutativity_k6_bvfunc_1,existence_m1_fraenkel,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k12_bvfunc_1,dt_k1_funct_2,dt_k3_valuat_1,dt_k6_bvfunc_1,dt_m1_fraenkel,dt_m1_subset_1,dt_m2_relset_1,cc1_margrel1,cc1_valuat_1,fc1_fraenkel,commutativity_k8_bvfunc_1,existence_m2_fraenkel,redefinition_k14_bvfunc_1,redefinition_k1_fraenkel,redefinition_k5_valuat_1,redefinition_k8_bvfunc_1,redefinition_m2_fraenkel,dt_k14_bvfunc_1,dt_k1_fraenkel,dt_k5_valuat_1,dt_k6_margrel1,dt_k8_bvfunc_1,dt_m2_fraenkel,dt_c1_9__bvfunc25,dt_c2_9__bvfunc25,dt_c3_9__bvfunc25,dt_c4_9__bvfunc25,fc3_margrel1,t8_bvfunc_4]),
    [interesting(0.65),file(bvfunc25,e11_9_1__bvfunc25),[file(bvfunc25,e11_9_1__bvfunc25)]]).

fof(e12_9_1__bvfunc25,plain,(
    k8_bvfunc_1(c1_9__bvfunc25,k5_valuat_1(c1_9__bvfunc25,c2_9__bvfunc25),k14_bvfunc_1(c1_9__bvfunc25,c3_9__bvfunc25,c4_9__bvfunc25)) = k14_bvfunc_1(c1_9__bvfunc25,c2_9__bvfunc25,k14_bvfunc_1(c1_9__bvfunc25,c3_9__bvfunc25,c4_9__bvfunc25)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_9__bvfunc25,dt_c2_9__bvfunc25,dt_c3_9__bvfunc25,dt_c4_9__bvfunc25])],[existence_m1_relset_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_fraenkel,fc3_valuat_1,rc1_fraenkel,rc1_valuat_1,rc2_margrel1,commutativity_k6_bvfunc_1,existence_m1_fraenkel,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k12_bvfunc_1,dt_k1_funct_2,dt_k3_valuat_1,dt_k6_bvfunc_1,dt_m1_fraenkel,dt_m1_subset_1,dt_m2_relset_1,cc1_margrel1,cc1_valuat_1,fc1_fraenkel,commutativity_k8_bvfunc_1,existence_m2_fraenkel,redefinition_k14_bvfunc_1,redefinition_k1_fraenkel,redefinition_k5_valuat_1,redefinition_k8_bvfunc_1,redefinition_m2_fraenkel,dt_k14_bvfunc_1,dt_k1_fraenkel,dt_k5_valuat_1,dt_k6_margrel1,dt_k8_bvfunc_1,dt_m2_fraenkel,dt_c1_9__bvfunc25,dt_c2_9__bvfunc25,dt_c3_9__bvfunc25,dt_c4_9__bvfunc25,fc3_margrel1,t8_bvfunc_4]),
    [interesting(0.65),file(bvfunc25,e12_9_1__bvfunc25),[file(bvfunc25,e12_9_1__bvfunc25)]]).

fof(e1_9__bvfunc25,plain,(
    k14_bvfunc_1(c1_9__bvfunc25,k14_bvfunc_1(c1_9__bvfunc25,c2_9__bvfunc25,c3_9__bvfunc25),k14_bvfunc_1(c1_9__bvfunc25,c2_9__bvfunc25,c4_9__bvfunc25)) = k14_bvfunc_1(c1_9__bvfunc25,c2_9__bvfunc25,k14_bvfunc_1(c1_9__bvfunc25,c3_9__bvfunc25,c4_9__bvfunc25)) ),
    inference(iterative_eq,[status(thm),assumptions([dt_c1_9__bvfunc25,dt_c2_9__bvfunc25,dt_c3_9__bvfunc25,dt_c4_9__bvfunc25])],[e1_9_1__bvfunc25,e2_9_1__bvfunc25,e3_9_1__bvfunc25,e4_9_1__bvfunc25,e5_9_1__bvfunc25,e6_9_1__bvfunc25,e7_9_1__bvfunc25,e8_9_1__bvfunc25,e9_9_1__bvfunc25,e10_9_1__bvfunc25,e11_9_1__bvfunc25,e12_9_1__bvfunc25]),
    [interesting(0.8),file(bvfunc25,e1_9__bvfunc25),[file(bvfunc25,e1_9__bvfunc25)]]).

fof(i5_9__bvfunc25,theorem,(
    $true ),
    introduced(tautology,[file(bvfunc25,i5_9__bvfunc25)]),
    [interesting(0.8),trivial,file(bvfunc25,i5_9__bvfunc25)]).

fof(i4_9__bvfunc25,plain,(
    k14_bvfunc_1(c1_9__bvfunc25,c2_9__bvfunc25,k14_bvfunc_1(c1_9__bvfunc25,c3_9__bvfunc25,c4_9__bvfunc25)) = k14_bvfunc_1(c1_9__bvfunc25,k14_bvfunc_1(c1_9__bvfunc25,c2_9__bvfunc25,c3_9__bvfunc25),k14_bvfunc_1(c1_9__bvfunc25,c2_9__bvfunc25,c4_9__bvfunc25)) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_9__bvfunc25,dt_c2_9__bvfunc25,dt_c3_9__bvfunc25,dt_c4_9__bvfunc25])],[e1_9__bvfunc25,i5_9__bvfunc25]),
    [interesting(0.8),file(bvfunc25,i4_9__bvfunc25),[file(bvfunc25,i4_9__bvfunc25)]]).

fof(i4_9_tmp__bvfunc25,plain,
    ( m2_fraenkel(c4_9__bvfunc25,c1_9__bvfunc25,k6_margrel1,k1_fraenkel(c1_9__bvfunc25,k6_margrel1))
   => k14_bvfunc_1(c1_9__bvfunc25,c2_9__bvfunc25,k14_bvfunc_1(c1_9__bvfunc25,c3_9__bvfunc25,c4_9__bvfunc25)) = k14_bvfunc_1(c1_9__bvfunc25,k14_bvfunc_1(c1_9__bvfunc25,c2_9__bvfunc25,c3_9__bvfunc25),k14_bvfunc_1(c1_9__bvfunc25,c2_9__bvfunc25,c4_9__bvfunc25)) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_9__bvfunc25,dt_c2_9__bvfunc25,dt_c3_9__bvfunc25]),discharge_asm(discharge,[dt_c4_9__bvfunc25])],[dt_c4_9__bvfunc25,i4_9__bvfunc25]),
    [interesting(0.8),i3_9__bvfunc25]).

fof(i3_9__bvfunc25,plain,(
    ! [A] : 
      ( m2_fraenkel(A,c1_9__bvfunc25,k6_margrel1,k1_fraenkel(c1_9__bvfunc25,k6_margrel1))
     => k14_bvfunc_1(c1_9__bvfunc25,c2_9__bvfunc25,k14_bvfunc_1(c1_9__bvfunc25,c3_9__bvfunc25,A)) = k14_bvfunc_1(c1_9__bvfunc25,k14_bvfunc_1(c1_9__bvfunc25,c2_9__bvfunc25,c3_9__bvfunc25),k14_bvfunc_1(c1_9__bvfunc25,c2_9__bvfunc25,A)) ) ),
    inference(let,[status(thm),assumptions([dt_c1_9__bvfunc25,dt_c2_9__bvfunc25,dt_c3_9__bvfunc25])],[i4_9_tmp__bvfunc25,dh_c4_9__bvfunc25]),
    [interesting(0.8),file(bvfunc25,i3_9__bvfunc25),[file(bvfunc25,i3_9__bvfunc25)]]).

fof(i3_9_tmp__bvfunc25,plain,
    ( m2_fraenkel(c3_9__bvfunc25,c1_9__bvfunc25,k6_margrel1,k1_fraenkel(c1_9__bvfunc25,k6_margrel1))
   => ! [A] : 
        ( m2_fraenkel(A,c1_9__bvfunc25,k6_margrel1,k1_fraenkel(c1_9__bvfunc25,k6_margrel1))
       => k14_bvfunc_1(c1_9__bvfunc25,c2_9__bvfunc25,k14_bvfunc_1(c1_9__bvfunc25,c3_9__bvfunc25,A)) = k14_bvfunc_1(c1_9__bvfunc25,k14_bvfunc_1(c1_9__bvfunc25,c2_9__bvfunc25,c3_9__bvfunc25),k14_bvfunc_1(c1_9__bvfunc25,c2_9__bvfunc25,A)) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_9__bvfunc25,dt_c2_9__bvfunc25]),discharge_asm(discharge,[dt_c3_9__bvfunc25])],[dt_c3_9__bvfunc25,i3_9__bvfunc25]),
    [interesting(0.8),i2_9__bvfunc25]).

fof(i2_9__bvfunc25,plain,(
    ! [A] : 
      ( m2_fraenkel(A,c1_9__bvfunc25,k6_margrel1,k1_fraenkel(c1_9__bvfunc25,k6_margrel1))
     => ! [B] : 
          ( m2_fraenkel(B,c1_9__bvfunc25,k6_margrel1,k1_fraenkel(c1_9__bvfunc25,k6_margrel1))
         => k14_bvfunc_1(c1_9__bvfunc25,c2_9__bvfunc25,k14_bvfunc_1(c1_9__bvfunc25,A,B)) = k14_bvfunc_1(c1_9__bvfunc25,k14_bvfunc_1(c1_9__bvfunc25,c2_9__bvfunc25,A),k14_bvfunc_1(c1_9__bvfunc25,c2_9__bvfunc25,B)) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_9__bvfunc25,dt_c2_9__bvfunc25])],[i3_9_tmp__bvfunc25,dh_c3_9__bvfunc25]),
    [interesting(0.8),file(bvfunc25,i2_9__bvfunc25),[file(bvfunc25,i2_9__bvfunc25)]]).

fof(i2_9_tmp__bvfunc25,plain,
    ( m2_fraenkel(c2_9__bvfunc25,c1_9__bvfunc25,k6_margrel1,k1_fraenkel(c1_9__bvfunc25,k6_margrel1))
   => ! [A] : 
        ( m2_fraenkel(A,c1_9__bvfunc25,k6_margrel1,k1_fraenkel(c1_9__bvfunc25,k6_margrel1))
       => ! [B] : 
            ( m2_fraenkel(B,c1_9__bvfunc25,k6_margrel1,k1_fraenkel(c1_9__bvfunc25,k6_margrel1))
           => k14_bvfunc_1(c1_9__bvfunc25,c2_9__bvfunc25,k14_bvfunc_1(c1_9__bvfunc25,A,B)) = k14_bvfunc_1(c1_9__bvfunc25,k14_bvfunc_1(c1_9__bvfunc25,c2_9__bvfunc25,A),k14_bvfunc_1(c1_9__bvfunc25,c2_9__bvfunc25,B)) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_9__bvfunc25]),discharge_asm(discharge,[dt_c2_9__bvfunc25])],[dt_c2_9__bvfunc25,i2_9__bvfunc25]),
    [interesting(0.8),i1_9__bvfunc25]).

fof(i1_9__bvfunc25,plain,(
    ! [A] : 
      ( m2_fraenkel(A,c1_9__bvfunc25,k6_margrel1,k1_fraenkel(c1_9__bvfunc25,k6_margrel1))
     => ! [B] : 
          ( m2_fraenkel(B,c1_9__bvfunc25,k6_margrel1,k1_fraenkel(c1_9__bvfunc25,k6_margrel1))
         => ! [C] : 
              ( m2_fraenkel(C,c1_9__bvfunc25,k6_margrel1,k1_fraenkel(c1_9__bvfunc25,k6_margrel1))
             => k14_bvfunc_1(c1_9__bvfunc25,A,k14_bvfunc_1(c1_9__bvfunc25,B,C)) = k14_bvfunc_1(c1_9__bvfunc25,k14_bvfunc_1(c1_9__bvfunc25,A,B),k14_bvfunc_1(c1_9__bvfunc25,A,C)) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_9__bvfunc25])],[i2_9_tmp__bvfunc25,dh_c2_9__bvfunc25]),
    [interesting(0.8),file(bvfunc25,i1_9__bvfunc25),[file(bvfunc25,i1_9__bvfunc25)]]).

fof(i1_9_tmp__bvfunc25,plain,
    ( ~ v1_xboole_0(c1_9__bvfunc25)
   => ! [A] : 
        ( m2_fraenkel(A,c1_9__bvfunc25,k6_margrel1,k1_fraenkel(c1_9__bvfunc25,k6_margrel1))
       => ! [B] : 
            ( m2_fraenkel(B,c1_9__bvfunc25,k6_margrel1,k1_fraenkel(c1_9__bvfunc25,k6_margrel1))
           => ! [C] : 
                ( m2_fraenkel(C,c1_9__bvfunc25,k6_margrel1,k1_fraenkel(c1_9__bvfunc25,k6_margrel1))
               => k14_bvfunc_1(c1_9__bvfunc25,A,k14_bvfunc_1(c1_9__bvfunc25,B,C)) = k14_bvfunc_1(c1_9__bvfunc25,k14_bvfunc_1(c1_9__bvfunc25,A,B),k14_bvfunc_1(c1_9__bvfunc25,A,C)) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_9__bvfunc25])],[dt_c1_9__bvfunc25,i1_9__bvfunc25]),
    [interesting(1),t9_bvfunc25]).

fof(t9_bvfunc25,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))
                 => k14_bvfunc_1(A,B,k14_bvfunc_1(A,C,D)) = k14_bvfunc_1(A,k14_bvfunc_1(A,B,C),k14_bvfunc_1(A,B,D)) ) ) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_9_tmp__bvfunc25,dh_c1_9__bvfunc25]),
    [interesting(1),file(bvfunc25,t9_bvfunc25),[file(bvfunc25,t9_bvfunc25)]]).