% Mizar ND problem: t1_bvfunc14,bvfunc14,29,54 
fof(dh_c1_1__bvfunc14,definition,
    ( ( ~ v1_xboole_0(c1_1__bvfunc14)
     => ! [A] : 
          ( m1_subset_1(A,c1_1__bvfunc14)
         => ! [B] : 
              ( m1_eqrel_1(B,c1_1__bvfunc14)
             => ! [C] : 
                  ( m1_eqrel_1(C,c1_1__bvfunc14)
                 => k22_bvfunc_1(c1_1__bvfunc14,A,k2_partit1(c1_1__bvfunc14,B,C)) = k5_subset_1(c1_1__bvfunc14,k22_bvfunc_1(c1_1__bvfunc14,A,B),k22_bvfunc_1(c1_1__bvfunc14,A,C)) ) ) ) )
   => ! [D] : 
        ( ~ v1_xboole_0(D)
       => ! [E] : 
            ( m1_subset_1(E,D)
           => ! [F] : 
                ( m1_eqrel_1(F,D)
               => ! [G] : 
                    ( m1_eqrel_1(G,D)
                   => k22_bvfunc_1(D,E,k2_partit1(D,F,G)) = k5_subset_1(D,k22_bvfunc_1(D,E,F),k22_bvfunc_1(D,E,G)) ) ) ) ) ),
    introduced(definition,[new_symbol(c1_1__bvfunc14),file(bvfunc14,c1_1__bvfunc14)]),
    [interesting(0.8),axiom,file(bvfunc14,c1_1__bvfunc14)]).

fof(dh_c2_1__bvfunc14,definition,
    ( ( m1_subset_1(c2_1__bvfunc14,c1_1__bvfunc14)
     => ! [A] : 
          ( m1_eqrel_1(A,c1_1__bvfunc14)
         => ! [B] : 
              ( m1_eqrel_1(B,c1_1__bvfunc14)
             => k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,k2_partit1(c1_1__bvfunc14,A,B)) = k5_subset_1(c1_1__bvfunc14,k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,A),k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,B)) ) ) )
   => ! [C] : 
        ( m1_subset_1(C,c1_1__bvfunc14)
       => ! [D] : 
            ( m1_eqrel_1(D,c1_1__bvfunc14)
           => ! [E] : 
                ( m1_eqrel_1(E,c1_1__bvfunc14)
               => k22_bvfunc_1(c1_1__bvfunc14,C,k2_partit1(c1_1__bvfunc14,D,E)) = k5_subset_1(c1_1__bvfunc14,k22_bvfunc_1(c1_1__bvfunc14,C,D),k22_bvfunc_1(c1_1__bvfunc14,C,E)) ) ) ) ),
    introduced(definition,[new_symbol(c2_1__bvfunc14),file(bvfunc14,c2_1__bvfunc14)]),
    [interesting(0.8),axiom,file(bvfunc14,c2_1__bvfunc14)]).

fof(dh_c3_1__bvfunc14,definition,
    ( ( m1_eqrel_1(c3_1__bvfunc14,c1_1__bvfunc14)
     => ! [A] : 
          ( m1_eqrel_1(A,c1_1__bvfunc14)
         => k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,k2_partit1(c1_1__bvfunc14,c3_1__bvfunc14,A)) = k5_subset_1(c1_1__bvfunc14,k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,c3_1__bvfunc14),k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,A)) ) )
   => ! [B] : 
        ( m1_eqrel_1(B,c1_1__bvfunc14)
       => ! [C] : 
            ( m1_eqrel_1(C,c1_1__bvfunc14)
           => k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,k2_partit1(c1_1__bvfunc14,B,C)) = k5_subset_1(c1_1__bvfunc14,k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,B),k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,C)) ) ) ),
    introduced(definition,[new_symbol(c3_1__bvfunc14),file(bvfunc14,c3_1__bvfunc14)]),
    [interesting(0.8),axiom,file(bvfunc14,c3_1__bvfunc14)]).

fof(dh_c4_1__bvfunc14,definition,
    ( ( m1_eqrel_1(c4_1__bvfunc14,c1_1__bvfunc14)
     => k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,k2_partit1(c1_1__bvfunc14,c3_1__bvfunc14,c4_1__bvfunc14)) = k5_subset_1(c1_1__bvfunc14,k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,c3_1__bvfunc14),k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,c4_1__bvfunc14)) )
   => ! [A] : 
        ( m1_eqrel_1(A,c1_1__bvfunc14)
       => k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,k2_partit1(c1_1__bvfunc14,c3_1__bvfunc14,A)) = k5_subset_1(c1_1__bvfunc14,k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,c3_1__bvfunc14),k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,A)) ) ),
    introduced(definition,[new_symbol(c4_1__bvfunc14),file(bvfunc14,c4_1__bvfunc14)]),
    [interesting(0.8),axiom,file(bvfunc14,c4_1__bvfunc14)]).

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

fof(fc1_xboole_0,theorem,(
    v1_xboole_0(k1_xboole_0) ),
    file(xboole_0,fc1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,fc1_xboole_0)]).

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(t2_boole,theorem,(
    ! [A] : k3_xboole_0(A,k1_xboole_0) = k1_xboole_0 ),
    file(boole,t2_boole),
    [interesting(0.9),axiom,file(boole,t2_boole)]).

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(commutativity_k3_xboole_0,theorem,(
    ! [A,B] : k3_xboole_0(A,B) = k3_xboole_0(B,A) ),
    file(xboole_0,k3_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k3_xboole_0)]).

fof(idempotence_k3_xboole_0,theorem,(
    ! [A,B] : k3_xboole_0(A,A) = A ),
    file(xboole_0,k3_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k3_xboole_0)]).

fof(existence_m1_bvfunc_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_eqrel_1(B,A) )
     => ? [C] : m1_bvfunc_1(C,A,B) ) ),
    file(bvfunc_1,m1_bvfunc_1),
    [interesting(0.9),axiom,file(bvfunc_1,m1_bvfunc_1)]).

fof(existence_m1_eqrel_1,axiom,(
    ! [A] : 
    ? [B] : m1_eqrel_1(B,A) ),
    file(eqrel_1,m1_eqrel_1),
    [interesting(0.9),axiom,file(eqrel_1,m1_eqrel_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(redefinition_m1_bvfunc_1,definition,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_eqrel_1(B,A) )
     => ! [C] : 
          ( m1_bvfunc_1(C,A,B)
        <=> m1_subset_1(C,B) ) ) ),
    file(bvfunc_1,m1_bvfunc_1),
    [interesting(0.9),axiom,file(bvfunc_1,m1_bvfunc_1)]).

fof(dt_k1_t_1topsp,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A)
        & m1_eqrel_1(C,A) )
     => m1_subset_1(k1_t_1topsp(A,B,C),k1_zfmisc_1(A)) ) ),
    file(t_1topsp,k1_t_1topsp),
    [interesting(0.9),axiom,file(t_1topsp,k1_t_1topsp)]).

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_xboole_0,axiom,(
    $true ),
    file(xboole_0,k3_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k3_xboole_0)]).

fof(dt_m1_bvfunc_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_eqrel_1(B,A) )
     => ! [C] : 
          ( m1_bvfunc_1(C,A,B)
         => m1_subset_1(C,k1_zfmisc_1(A)) ) ) ),
    file(bvfunc_1,m1_bvfunc_1),
    [interesting(0.9),axiom,file(bvfunc_1,m1_bvfunc_1)]).

fof(dt_m1_eqrel_1,axiom,(
    ! [A,B] : 
      ( m1_eqrel_1(B,A)
     => m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) ) ),
    file(eqrel_1,m1_eqrel_1),
    [interesting(0.9),axiom,file(eqrel_1,m1_eqrel_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(cc1_eqrel_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_eqrel_1(B,A)
         => ~ v1_xboole_0(B) ) ) ),
    file(eqrel_1,cc1_eqrel_1),
    [interesting(0.9),axiom,file(eqrel_1,cc1_eqrel_1)]).

fof(cc2_eqrel_1,theorem,(
    ! [A,B] : 
      ( m1_eqrel_1(B,A)
     => v1_setfam_1(B) ) ),
    file(eqrel_1,cc2_eqrel_1),
    [interesting(0.9),axiom,file(eqrel_1,cc2_eqrel_1)]).

fof(fc1_subset_1,theorem,(
    ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ),
    file(subset_1,fc1_subset_1),
    [interesting(0.9),axiom,file(subset_1,fc1_subset_1)]).

fof(rc1_subset_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B) ) ) ),
    file(subset_1,rc1_subset_1),
    [interesting(0.9),axiom,file(subset_1,rc1_subset_1)]).

fof(rc1_xboole_0,theorem,(
    ? [A] : v1_xboole_0(A) ),
    file(xboole_0,rc1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,rc1_xboole_0)]).

fof(rc2_subset_1,theorem,(
    ! [A] : 
    ? [B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
      & v1_xboole_0(B) ) ),
    file(subset_1,rc2_subset_1),
    [interesting(0.9),axiom,file(subset_1,rc2_subset_1)]).

fof(rc2_xboole_0,theorem,(
    ? [A] : ~ v1_xboole_0(A) ),
    file(xboole_0,rc2_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,rc2_xboole_0)]).

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(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(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(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_k2_partit1,theorem,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & m1_eqrel_1(B,A)
        & m1_eqrel_1(C,A) )
     => k2_partit1(A,B,C) = k2_partit1(A,C,B) ) ),
    file(partit1,k2_partit1),
    [interesting(0.9),axiom,file(partit1,k2_partit1)]).

fof(commutativity_k5_subset_1,theorem,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k5_subset_1(A,B,C) = k5_subset_1(A,C,B) ) ),
    file(subset_1,k5_subset_1),
    [interesting(0.9),axiom,file(subset_1,k5_subset_1)]).

fof(idempotence_k5_subset_1,theorem,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k5_subset_1(A,B,B) = B ) ),
    file(subset_1,k5_subset_1),
    [interesting(0.9),axiom,file(subset_1,k5_subset_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(redefinition_k22_bvfunc_1,definition,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A)
        & m1_eqrel_1(C,A) )
     => k22_bvfunc_1(A,B,C) = k1_t_1topsp(A,B,C) ) ),
    file(bvfunc_1,k22_bvfunc_1),
    [interesting(0.9),axiom,file(bvfunc_1,k22_bvfunc_1)]).

fof(redefinition_k5_subset_1,definition,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k5_subset_1(A,B,C) = k3_xboole_0(B,C) ) ),
    file(subset_1,k5_subset_1),
    [interesting(0.9),axiom,file(subset_1,k5_subset_1)]).

fof(dt_k22_bvfunc_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A)
        & m1_eqrel_1(C,A) )
     => m1_bvfunc_1(k22_bvfunc_1(A,B,C),A,C) ) ),
    file(bvfunc_1,k22_bvfunc_1),
    [interesting(0.9),axiom,file(bvfunc_1,k22_bvfunc_1)]).

fof(dt_k2_partit1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & m1_eqrel_1(B,A)
        & m1_eqrel_1(C,A) )
     => m1_eqrel_1(k2_partit1(A,B,C),A) ) ),
    file(partit1,k2_partit1),
    [interesting(0.9),axiom,file(partit1,k2_partit1)]).

fof(dt_k5_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => m1_subset_1(k5_subset_1(A,B,C),k1_zfmisc_1(A)) ) ),
    file(subset_1,k5_subset_1),
    [interesting(0.9),axiom,file(subset_1,k5_subset_1)]).

fof(dt_c1_1__bvfunc14,assumption,(
    ~ v1_xboole_0(c1_1__bvfunc14) ),
    introduced(assumption,[file(bvfunc14,c1_1__bvfunc14)]),
    [interesting(0.8),axiom,file(bvfunc14,c1_1__bvfunc14)]).

fof(dt_c2_1__bvfunc14,assumption,(
    m1_subset_1(c2_1__bvfunc14,c1_1__bvfunc14) ),
    introduced(assumption,[file(bvfunc14,c2_1__bvfunc14)]),
    [interesting(0.8),axiom,file(bvfunc14,c2_1__bvfunc14)]).

fof(dt_c3_1__bvfunc14,assumption,(
    m1_eqrel_1(c3_1__bvfunc14,c1_1__bvfunc14) ),
    introduced(assumption,[file(bvfunc14,c3_1__bvfunc14)]),
    [interesting(0.8),axiom,file(bvfunc14,c3_1__bvfunc14)]).

fof(dt_c4_1__bvfunc14,assumption,(
    m1_eqrel_1(c4_1__bvfunc14,c1_1__bvfunc14) ),
    introduced(assumption,[file(bvfunc14,c4_1__bvfunc14)]),
    [interesting(0.8),axiom,file(bvfunc14,c4_1__bvfunc14)]).

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(dt_c1_1_2__bvfunc14,assumption,(
    $true ),
    introduced(assumption,[file(bvfunc14,c1_1_2__bvfunc14)]),
    [interesting(0.65),axiom,file(bvfunc14,c1_1_2__bvfunc14)]).

fof(d3_tarski,definition,(
    ! [A,B] : 
      ( r1_tarski(A,B)
    <=> ! [C] : 
          ( r2_hidden(C,A)
         => r2_hidden(C,B) ) ) ),
    file(tarski,d3_tarski),
    [interesting(0.9),axiom,file(tarski,d3_tarski)]).

fof(dh_c1_1_2__bvfunc14,definition,
    ( ~ ( r2_hidden(c1_1_2__bvfunc14,k5_subset_1(c1_1__bvfunc14,k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,c3_1__bvfunc14),k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,c4_1__bvfunc14)))
        & ~ r2_hidden(c1_1_2__bvfunc14,k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,k2_partit1(c1_1__bvfunc14,c3_1__bvfunc14,c4_1__bvfunc14))) )
   => ! [A] : 
        ~ ( r2_hidden(A,k5_subset_1(c1_1__bvfunc14,k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,c3_1__bvfunc14),k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,c4_1__bvfunc14)))
          & ~ r2_hidden(A,k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,k2_partit1(c1_1__bvfunc14,c3_1__bvfunc14,c4_1__bvfunc14))) ) ),
    introduced(definition,[new_symbol(c1_1_2__bvfunc14),file(bvfunc14,c1_1_2__bvfunc14)]),
    [interesting(0.65),axiom,file(bvfunc14,c1_1_2__bvfunc14)]).

fof(e1_1_2__bvfunc14,assumption,(
    r2_hidden(c1_1_2__bvfunc14,k5_subset_1(c1_1__bvfunc14,k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,c3_1__bvfunc14),k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,c4_1__bvfunc14))) ),
    introduced(assumption,[file(bvfunc14,e1_1_2__bvfunc14)]),
    [interesting(0.65),axiom,file(bvfunc14,e1_1_2__bvfunc14)]).

fof(symmetry_r1_xboole_0,theorem,(
    ! [A,B] : 
      ( r1_xboole_0(A,B)
     => r1_xboole_0(B,A) ) ),
    file(xboole_0,r1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,r1_xboole_0)]).

fof(de_c2_1_2__bvfunc14,definition,(
    c2_1_2__bvfunc14 = c1_1_2__bvfunc14 ),
    introduced(definition,[new_symbol(c2_1_2__bvfunc14),file(bvfunc14,c2_1_2__bvfunc14)]),
    [interesting(0.65),axiom,file(bvfunc14,c2_1_2__bvfunc14)]).

fof(e2_1_2__bvfunc14,plain,(
    m1_subset_1(c1_1_2__bvfunc14,c1_1__bvfunc14) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_1__bvfunc14,dt_c1_1_2__bvfunc14,dt_c2_1__bvfunc14,dt_c3_1__bvfunc14,dt_c4_1__bvfunc14,e1_1_2__bvfunc14])],[reflexivity_r1_tarski,dt_k1_xboole_0,fc1_xboole_0,t2_boole,commutativity_k3_xboole_0,idempotence_k3_xboole_0,existence_m1_bvfunc_1,existence_m1_eqrel_1,redefinition_m1_bvfunc_1,dt_k1_t_1topsp,dt_k1_zfmisc_1,dt_k3_xboole_0,dt_m1_bvfunc_1,dt_m1_eqrel_1,cc1_eqrel_1,cc2_eqrel_1,fc1_subset_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,commutativity_k5_subset_1,idempotence_k5_subset_1,antisymmetry_r2_hidden,existence_m1_subset_1,redefinition_k22_bvfunc_1,redefinition_k5_subset_1,dt_k22_bvfunc_1,dt_k5_subset_1,dt_m1_subset_1,dt_c1_1__bvfunc14,dt_c1_1_2__bvfunc14,dt_c2_1__bvfunc14,dt_c3_1__bvfunc14,dt_c4_1__bvfunc14,t1_subset,t7_boole,e1_1_2__bvfunc14]),
    [interesting(0.65),file(bvfunc14,e2_1_2__bvfunc14),[file(bvfunc14,e2_1_2__bvfunc14)]]).

fof(dt_c2_1_2__bvfunc14,plain,(
    m1_subset_1(c2_1_2__bvfunc14,c1_1__bvfunc14) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_1__bvfunc14,dt_c1_1_2__bvfunc14,dt_c2_1__bvfunc14,dt_c3_1__bvfunc14,dt_c4_1__bvfunc14,e1_1_2__bvfunc14])],[antisymmetry_r2_hidden,dt_k1_xboole_0,fc1_xboole_0,t1_subset,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_subset_1,dt_m1_subset_1,dt_c1_1__bvfunc14,dt_c1_1_2__bvfunc14,de_c2_1_2__bvfunc14,e2_1_2__bvfunc14]),
    [interesting(0.65),file(bvfunc14,c2_1_2__bvfunc14),[file(bvfunc14,c2_1_2__bvfunc14)]]).

fof(dh_c4_1_2__bvfunc14,definition,
    ( ? [A,B] : 
        ( r2_hidden(A,c3_1__bvfunc14)
        & r2_hidden(B,c4_1__bvfunc14)
        & k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,k2_partit1(c1_1__bvfunc14,c3_1__bvfunc14,c4_1__bvfunc14)) = k3_xboole_0(A,B) )
   => ? [C] : 
        ( r2_hidden(c4_1_2__bvfunc14,c3_1__bvfunc14)
        & r2_hidden(C,c4_1__bvfunc14)
        & k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,k2_partit1(c1_1__bvfunc14,c3_1__bvfunc14,c4_1__bvfunc14)) = k3_xboole_0(c4_1_2__bvfunc14,C) ) ),
    introduced(definition,[new_symbol(c4_1_2__bvfunc14),file(bvfunc14,c4_1_2__bvfunc14)]),
    [interesting(0.65),axiom,file(bvfunc14,c4_1_2__bvfunc14)]).

fof(commutativity_k3_setfam_1,theorem,(
    ! [A,B] : k3_setfam_1(A,B) = k3_setfam_1(B,A) ),
    file(setfam_1,k3_setfam_1),
    [interesting(0.9),axiom,file(setfam_1,k3_setfam_1)]).

fof(dt_k1_tarski,axiom,(
    $true ),
    file(tarski,k1_tarski),
    [interesting(0.9),axiom,file(tarski,k1_tarski)]).

fof(dt_k3_setfam_1,axiom,(
    $true ),
    file(setfam_1,k3_setfam_1),
    [interesting(0.9),axiom,file(setfam_1,k3_setfam_1)]).

fof(fc2_subset_1,theorem,(
    ! [A] : ~ v1_xboole_0(k1_tarski(A)) ),
    file(subset_1,fc2_subset_1),
    [interesting(0.9),axiom,file(subset_1,fc2_subset_1)]).

fof(dt_k4_xboole_0,axiom,(
    $true ),
    file(xboole_0,k4_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k4_xboole_0)]).

fof(t3_boole,theorem,(
    ! [A] : k4_xboole_0(A,k1_xboole_0) = A ),
    file(boole,t3_boole),
    [interesting(0.9),axiom,file(boole,t3_boole)]).

fof(t4_boole,theorem,(
    ! [A] : k4_xboole_0(k1_xboole_0,A) = k1_xboole_0 ),
    file(boole,t4_boole),
    [interesting(0.9),axiom,file(boole,t4_boole)]).

fof(d4_partit1,definition,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_eqrel_1(B,A)
         => ! [C] : 
              ( m1_eqrel_1(C,A)
             => k2_partit1(A,B,C) = k4_xboole_0(k3_setfam_1(B,C),k1_tarski(k1_xboole_0)) ) ) ) ),
    file(partit1,d4_partit1),
    [interesting(0.9),axiom,file(partit1,d4_partit1)]).

fof(e10_1_2__bvfunc14,plain,(
    k2_partit1(c1_1__bvfunc14,c3_1__bvfunc14,c4_1__bvfunc14) = k4_xboole_0(k3_setfam_1(c3_1__bvfunc14,c4_1__bvfunc14),k1_tarski(k1_xboole_0)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_1__bvfunc14,dt_c3_1__bvfunc14,dt_c4_1__bvfunc14])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,fc1_subset_1,rc1_subset_1,rc2_subset_1,t1_subset,t2_subset,t3_subset,t4_subset,t5_subset,commutativity_k2_partit1,commutativity_k3_setfam_1,existence_m1_eqrel_1,dt_k1_tarski,dt_k1_xboole_0,dt_k2_partit1,dt_k3_setfam_1,dt_k4_xboole_0,dt_m1_eqrel_1,dt_c1_1__bvfunc14,dt_c3_1__bvfunc14,dt_c4_1__bvfunc14,cc1_eqrel_1,cc2_eqrel_1,fc1_xboole_0,fc2_subset_1,rc1_xboole_0,rc2_xboole_0,t3_boole,t4_boole,t6_boole,t7_boole,t8_boole,d4_partit1]),
    [interesting(0.65),file(bvfunc14,e10_1_2__bvfunc14),[file(bvfunc14,e10_1_2__bvfunc14)]]).

fof(d4_xboole_0,definition,(
    ! [A,B,C] : 
      ( C = k4_xboole_0(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( r2_hidden(D,A)
            & ~ r2_hidden(D,B) ) ) ) ),
    file(xboole_0,d4_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,d4_xboole_0)]).

fof(e11_1_2__bvfunc14,plain,
    ( r2_hidden(k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,k2_partit1(c1_1__bvfunc14,c3_1__bvfunc14,c4_1__bvfunc14)),k3_setfam_1(c3_1__bvfunc14,c4_1__bvfunc14))
    & ~ r2_hidden(k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,k2_partit1(c1_1__bvfunc14,c3_1__bvfunc14,c4_1__bvfunc14)),k1_tarski(k1_xboole_0)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_1__bvfunc14,dt_c1_1__bvfunc14,dt_c3_1__bvfunc14,dt_c4_1__bvfunc14])],[reflexivity_r1_tarski,dt_k1_zfmisc_1,fc1_subset_1,rc1_subset_1,rc2_subset_1,t3_subset,t4_subset,t5_subset,existence_m1_bvfunc_1,existence_m1_eqrel_1,existence_m1_subset_1,redefinition_m1_bvfunc_1,dt_k1_t_1topsp,dt_m1_bvfunc_1,dt_m1_eqrel_1,dt_m1_subset_1,cc1_eqrel_1,cc2_eqrel_1,rc1_xboole_0,rc2_xboole_0,t2_subset,t8_boole,commutativity_k2_partit1,commutativity_k3_setfam_1,antisymmetry_r2_hidden,redefinition_k22_bvfunc_1,dt_k1_tarski,dt_k1_xboole_0,dt_k22_bvfunc_1,dt_k2_partit1,dt_k3_setfam_1,dt_k4_xboole_0,dt_c1_1__bvfunc14,dt_c2_1__bvfunc14,dt_c3_1__bvfunc14,dt_c4_1__bvfunc14,fc1_xboole_0,fc2_subset_1,t1_subset,t3_boole,t4_boole,t6_boole,t7_boole,e10_1_2__bvfunc14,d4_xboole_0]),
    [interesting(0.65),file(bvfunc14,e11_1_2__bvfunc14),[file(bvfunc14,e11_1_2__bvfunc14)]]).

fof(d5_setfam_1,definition,(
    ! [A,B,C] : 
      ( C = k3_setfam_1(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ? [E,F] : 
              ( r2_hidden(E,A)
              & r2_hidden(F,B)
              & D = k3_xboole_0(E,F) ) ) ) ),
    file(setfam_1,d5_setfam_1),
    [interesting(0.9),axiom,file(setfam_1,d5_setfam_1)]).

fof(e12_1_2__bvfunc14,plain,(
    ? [A,B] : 
      ( r2_hidden(A,c3_1__bvfunc14)
      & r2_hidden(B,c4_1__bvfunc14)
      & k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,k2_partit1(c1_1__bvfunc14,c3_1__bvfunc14,c4_1__bvfunc14)) = k3_xboole_0(A,B) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_1__bvfunc14,dt_c1_1__bvfunc14,dt_c3_1__bvfunc14,dt_c4_1__bvfunc14])],[reflexivity_r1_tarski,dt_k1_zfmisc_1,fc1_subset_1,rc1_subset_1,rc2_subset_1,t3_subset,t4_subset,t5_subset,existence_m1_bvfunc_1,existence_m1_eqrel_1,existence_m1_subset_1,redefinition_m1_bvfunc_1,dt_k1_t_1topsp,dt_m1_bvfunc_1,dt_m1_eqrel_1,dt_m1_subset_1,cc1_eqrel_1,cc2_eqrel_1,rc1_xboole_0,rc2_xboole_0,t2_subset,t8_boole,commutativity_k2_partit1,commutativity_k3_setfam_1,commutativity_k3_xboole_0,idempotence_k3_xboole_0,antisymmetry_r2_hidden,redefinition_k22_bvfunc_1,dt_k1_tarski,dt_k1_xboole_0,dt_k22_bvfunc_1,dt_k2_partit1,dt_k3_setfam_1,dt_k3_xboole_0,dt_c1_1__bvfunc14,dt_c2_1__bvfunc14,dt_c3_1__bvfunc14,dt_c4_1__bvfunc14,fc1_xboole_0,fc2_subset_1,t1_subset,t2_boole,t6_boole,t7_boole,e11_1_2__bvfunc14,d5_setfam_1]),
    [interesting(0.65),file(bvfunc14,e12_1_2__bvfunc14),[file(bvfunc14,e12_1_2__bvfunc14)]]).

fof(dt_c4_1_2__bvfunc14,plain,(
    $true ),
    inference(consider,[status(thm),assumptions([dt_c2_1__bvfunc14,dt_c1_1__bvfunc14,dt_c3_1__bvfunc14,dt_c4_1__bvfunc14])],[dh_c4_1_2__bvfunc14,e12_1_2__bvfunc14]),
    [interesting(0.65),file(bvfunc14,c4_1_2__bvfunc14),[file(bvfunc14,c4_1_2__bvfunc14)]]).

fof(dh_c5_1_2__bvfunc14,definition,
    ( ? [A] : 
        ( r2_hidden(c4_1_2__bvfunc14,c3_1__bvfunc14)
        & r2_hidden(A,c4_1__bvfunc14)
        & k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,k2_partit1(c1_1__bvfunc14,c3_1__bvfunc14,c4_1__bvfunc14)) = k3_xboole_0(c4_1_2__bvfunc14,A) )
   => ( r2_hidden(c4_1_2__bvfunc14,c3_1__bvfunc14)
      & r2_hidden(c5_1_2__bvfunc14,c4_1__bvfunc14)
      & k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,k2_partit1(c1_1__bvfunc14,c3_1__bvfunc14,c4_1__bvfunc14)) = k3_xboole_0(c4_1_2__bvfunc14,c5_1_2__bvfunc14) ) ),
    introduced(definition,[new_symbol(c5_1_2__bvfunc14),file(bvfunc14,c5_1_2__bvfunc14)]),
    [interesting(0.65),axiom,file(bvfunc14,c5_1_2__bvfunc14)]).

fof(dt_c5_1_2__bvfunc14,plain,(
    $true ),
    inference(consider,[status(thm),assumptions([dt_c2_1__bvfunc14,dt_c1_1__bvfunc14,dt_c3_1__bvfunc14,dt_c4_1__bvfunc14])],[dh_c4_1_2__bvfunc14,dh_c5_1_2__bvfunc14,e12_1_2__bvfunc14]),
    [interesting(0.65),file(bvfunc14,c5_1_2__bvfunc14),[file(bvfunc14,c5_1_2__bvfunc14)]]).

fof(d1_t_1topsp,definition,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ! [C] : 
              ( m1_eqrel_1(C,A)
             => ! [D] : 
                  ( m1_subset_1(D,k1_zfmisc_1(A))
                 => ( D = k1_t_1topsp(A,B,C)
                  <=> ( r2_hidden(B,D)
                      & r2_hidden(D,C) ) ) ) ) ) ) ),
    file(t_1topsp,d1_t_1topsp),
    [interesting(0.9),axiom,file(t_1topsp,d1_t_1topsp)]).

fof(e4_1_2__bvfunc14,plain,
    ( r2_hidden(c2_1_2__bvfunc14,k22_bvfunc_1(c1_1__bvfunc14,c2_1_2__bvfunc14,c3_1__bvfunc14))
    & r2_hidden(k22_bvfunc_1(c1_1__bvfunc14,c2_1_2__bvfunc14,c3_1__bvfunc14),c3_1__bvfunc14) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_1__bvfunc14,dt_c1_1_2__bvfunc14,dt_c2_1__bvfunc14,dt_c4_1__bvfunc14,e1_1_2__bvfunc14,dt_c3_1__bvfunc14])],[reflexivity_r1_tarski,existence_m1_bvfunc_1,redefinition_m1_bvfunc_1,dt_k1_xboole_0,dt_m1_bvfunc_1,dt_c1_1_2__bvfunc14,fc1_xboole_0,antisymmetry_r2_hidden,existence_m1_eqrel_1,existence_m1_subset_1,redefinition_k22_bvfunc_1,dt_k1_t_1topsp,dt_k1_zfmisc_1,dt_k22_bvfunc_1,dt_m1_eqrel_1,dt_m1_subset_1,dt_c1_1__bvfunc14,dt_c2_1_2__bvfunc14,dt_c3_1__bvfunc14,de_c2_1_2__bvfunc14,cc1_eqrel_1,cc2_eqrel_1,fc1_subset_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,t1_subset,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole,d1_t_1topsp]),
    [interesting(0.65),file(bvfunc14,e4_1_2__bvfunc14),[file(bvfunc14,e4_1_2__bvfunc14)]]).

fof(e5_1_2__bvfunc14,plain,
    ( r2_hidden(c2_1_2__bvfunc14,k22_bvfunc_1(c1_1__bvfunc14,c2_1_2__bvfunc14,c4_1__bvfunc14))
    & r2_hidden(k22_bvfunc_1(c1_1__bvfunc14,c2_1_2__bvfunc14,c4_1__bvfunc14),c4_1__bvfunc14) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_1__bvfunc14,dt_c1_1_2__bvfunc14,dt_c2_1__bvfunc14,dt_c3_1__bvfunc14,e1_1_2__bvfunc14,dt_c4_1__bvfunc14])],[reflexivity_r1_tarski,existence_m1_bvfunc_1,redefinition_m1_bvfunc_1,dt_k1_xboole_0,dt_m1_bvfunc_1,dt_c1_1_2__bvfunc14,fc1_xboole_0,antisymmetry_r2_hidden,existence_m1_eqrel_1,existence_m1_subset_1,redefinition_k22_bvfunc_1,dt_k1_t_1topsp,dt_k1_zfmisc_1,dt_k22_bvfunc_1,dt_m1_eqrel_1,dt_m1_subset_1,dt_c1_1__bvfunc14,dt_c2_1_2__bvfunc14,dt_c4_1__bvfunc14,de_c2_1_2__bvfunc14,cc1_eqrel_1,cc2_eqrel_1,fc1_subset_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,t1_subset,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole,d1_t_1topsp]),
    [interesting(0.65),file(bvfunc14,e5_1_2__bvfunc14),[file(bvfunc14,e5_1_2__bvfunc14)]]).

fof(d3_xboole_0,definition,(
    ! [A,B,C] : 
      ( C = k3_xboole_0(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( r2_hidden(D,A)
            & r2_hidden(D,B) ) ) ) ),
    file(xboole_0,d3_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,d3_xboole_0)]).

fof(e21_1_2__bvfunc14,plain,(
    r2_hidden(c2_1_2__bvfunc14,k5_subset_1(c1_1__bvfunc14,k22_bvfunc_1(c1_1__bvfunc14,c2_1_2__bvfunc14,c3_1__bvfunc14),k22_bvfunc_1(c1_1__bvfunc14,c2_1_2__bvfunc14,c4_1__bvfunc14))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_1__bvfunc14,dt_c1_1_2__bvfunc14,dt_c2_1__bvfunc14,dt_c3_1__bvfunc14,e1_1_2__bvfunc14,dt_c4_1__bvfunc14])],[reflexivity_r1_tarski,dt_k1_xboole_0,fc1_xboole_0,t2_boole,existence_m1_bvfunc_1,existence_m1_eqrel_1,existence_m1_subset_1,redefinition_m1_bvfunc_1,dt_k1_t_1topsp,dt_k1_zfmisc_1,dt_m1_bvfunc_1,dt_m1_eqrel_1,dt_m1_subset_1,dt_c1_1_2__bvfunc14,cc1_eqrel_1,cc2_eqrel_1,fc1_subset_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,commutativity_k3_xboole_0,idempotence_k3_xboole_0,commutativity_k5_subset_1,idempotence_k5_subset_1,antisymmetry_r2_hidden,redefinition_k22_bvfunc_1,redefinition_k5_subset_1,dt_k22_bvfunc_1,dt_k3_xboole_0,dt_k5_subset_1,dt_c1_1__bvfunc14,dt_c2_1_2__bvfunc14,dt_c3_1__bvfunc14,dt_c4_1__bvfunc14,de_c2_1_2__bvfunc14,t1_subset,t7_boole,e4_1_2__bvfunc14,e5_1_2__bvfunc14,d3_xboole_0]),
    [interesting(0.65),file(bvfunc14,e21_1_2__bvfunc14),[file(bvfunc14,e21_1_2__bvfunc14)]]).

fof(e3_1_2__bvfunc14,plain,
    ( r2_hidden(c2_1_2__bvfunc14,k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,c3_1__bvfunc14))
    & r2_hidden(c2_1_2__bvfunc14,k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,c4_1__bvfunc14)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_1__bvfunc14,dt_c1_1_2__bvfunc14,dt_c2_1__bvfunc14,dt_c3_1__bvfunc14,dt_c4_1__bvfunc14,e1_1_2__bvfunc14])],[reflexivity_r1_tarski,dt_k1_xboole_0,fc1_xboole_0,t2_boole,existence_m1_bvfunc_1,existence_m1_eqrel_1,existence_m1_subset_1,redefinition_m1_bvfunc_1,dt_k1_t_1topsp,dt_k1_zfmisc_1,dt_m1_bvfunc_1,dt_m1_eqrel_1,dt_m1_subset_1,cc1_eqrel_1,cc2_eqrel_1,fc1_subset_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,commutativity_k3_xboole_0,idempotence_k3_xboole_0,commutativity_k5_subset_1,idempotence_k5_subset_1,antisymmetry_r2_hidden,redefinition_k22_bvfunc_1,redefinition_k5_subset_1,dt_k22_bvfunc_1,dt_k3_xboole_0,dt_k5_subset_1,dt_c1_1__bvfunc14,dt_c1_1_2__bvfunc14,dt_c2_1__bvfunc14,dt_c2_1_2__bvfunc14,dt_c3_1__bvfunc14,dt_c4_1__bvfunc14,de_c2_1_2__bvfunc14,t1_subset,t7_boole,e1_1_2__bvfunc14,d3_xboole_0]),
    [interesting(0.65),file(bvfunc14,e3_1_2__bvfunc14),[file(bvfunc14,e3_1_2__bvfunc14)]]).

fof(t3_xboole_0,theorem,(
    ! [A,B] : 
      ( ~ ( ~ r1_xboole_0(A,B)
          & ! [C] : 
              ~ ( r2_hidden(C,A)
                & r2_hidden(C,B) ) )
      & ~ ( ? [C] : 
              ( r2_hidden(C,A)
              & r2_hidden(C,B) )
          & r1_xboole_0(A,B) ) ) ),
    file(xboole_0,t3_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,t3_xboole_0)]).

fof(e7_1_2__bvfunc14,plain,(
    ~ r1_xboole_0(k22_bvfunc_1(c1_1__bvfunc14,c2_1_2__bvfunc14,c4_1__bvfunc14),k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,c4_1__bvfunc14)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_1__bvfunc14,dt_c1_1_2__bvfunc14,dt_c2_1__bvfunc14,dt_c3_1__bvfunc14,e1_1_2__bvfunc14,dt_c4_1__bvfunc14])],[reflexivity_r1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,fc1_subset_1,fc1_xboole_0,rc1_subset_1,rc2_subset_1,t3_subset,t4_subset,t5_subset,existence_m1_bvfunc_1,existence_m1_eqrel_1,existence_m1_subset_1,redefinition_m1_bvfunc_1,dt_k1_t_1topsp,dt_m1_bvfunc_1,dt_m1_eqrel_1,dt_m1_subset_1,dt_c1_1_2__bvfunc14,cc1_eqrel_1,cc2_eqrel_1,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t8_boole,symmetry_r1_xboole_0,antisymmetry_r2_hidden,redefinition_k22_bvfunc_1,dt_k22_bvfunc_1,dt_c1_1__bvfunc14,dt_c2_1__bvfunc14,dt_c2_1_2__bvfunc14,dt_c3_1__bvfunc14,dt_c4_1__bvfunc14,de_c2_1_2__bvfunc14,t1_subset,t7_boole,e3_1_2__bvfunc14,e5_1_2__bvfunc14,t3_xboole_0]),
    [interesting(0.65),file(bvfunc14,e7_1_2__bvfunc14),[file(bvfunc14,e7_1_2__bvfunc14)]]).

fof(e13_1_2__bvfunc14,plain,
    ( r2_hidden(c4_1_2__bvfunc14,c3_1__bvfunc14)
    & r2_hidden(c5_1_2__bvfunc14,c4_1__bvfunc14)
    & k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,k2_partit1(c1_1__bvfunc14,c3_1__bvfunc14,c4_1__bvfunc14)) = k3_xboole_0(c4_1_2__bvfunc14,c5_1_2__bvfunc14) ),
    inference(consider,[status(thm),assumptions([dt_c2_1__bvfunc14,dt_c1_1__bvfunc14,dt_c3_1__bvfunc14,dt_c4_1__bvfunc14])],[dh_c4_1_2__bvfunc14,dh_c5_1_2__bvfunc14,e12_1_2__bvfunc14]),
    [interesting(0.65),file(bvfunc14,e13_1_2__bvfunc14),[file(bvfunc14,e13_1_2__bvfunc14)]]).

fof(dt_k3_tarski,axiom,(
    $true ),
    file(tarski,k3_tarski),
    [interesting(0.9),axiom,file(tarski,k3_tarski)]).

fof(redefinition_k5_setfam_1,definition,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => k5_setfam_1(A,B) = k3_tarski(B) ) ),
    file(setfam_1,k5_setfam_1),
    [interesting(0.9),axiom,file(setfam_1,k5_setfam_1)]).

fof(dt_k5_setfam_1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => m1_subset_1(k5_setfam_1(A,B),k1_zfmisc_1(A)) ) ),
    file(setfam_1,k5_setfam_1),
    [interesting(0.9),axiom,file(setfam_1,k5_setfam_1)]).

fof(e9_1_2__bvfunc14,plain,
    ( r2_hidden(c2_1__bvfunc14,k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,c4_1__bvfunc14))
    & r2_hidden(k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,c4_1__bvfunc14),c4_1__bvfunc14) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_1__bvfunc14,dt_c2_1__bvfunc14,dt_c4_1__bvfunc14])],[reflexivity_r1_tarski,existence_m1_bvfunc_1,redefinition_m1_bvfunc_1,dt_k1_xboole_0,dt_m1_bvfunc_1,fc1_xboole_0,antisymmetry_r2_hidden,existence_m1_eqrel_1,existence_m1_subset_1,redefinition_k22_bvfunc_1,dt_k1_t_1topsp,dt_k1_zfmisc_1,dt_k22_bvfunc_1,dt_m1_eqrel_1,dt_m1_subset_1,dt_c1_1__bvfunc14,dt_c2_1__bvfunc14,dt_c4_1__bvfunc14,cc1_eqrel_1,cc2_eqrel_1,fc1_subset_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,t1_subset,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole,d1_t_1topsp]),
    [interesting(0.65),file(bvfunc14,e9_1_2__bvfunc14),[file(bvfunc14,e9_1_2__bvfunc14)]]).

fof(e14_1_2__bvfunc14,plain,(
    r2_hidden(c2_1__bvfunc14,k3_xboole_0(c4_1_2__bvfunc14,c5_1_2__bvfunc14)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_1__bvfunc14,dt_c1_1__bvfunc14,dt_c3_1__bvfunc14,dt_c4_1__bvfunc14])],[reflexivity_r1_tarski,existence_m1_bvfunc_1,redefinition_m1_bvfunc_1,dt_k1_xboole_0,dt_m1_bvfunc_1,fc1_xboole_0,t2_boole,commutativity_k2_partit1,commutativity_k3_xboole_0,idempotence_k3_xboole_0,antisymmetry_r2_hidden,existence_m1_eqrel_1,existence_m1_subset_1,redefinition_k22_bvfunc_1,dt_k1_t_1topsp,dt_k1_zfmisc_1,dt_k22_bvfunc_1,dt_k2_partit1,dt_k3_xboole_0,dt_m1_eqrel_1,dt_m1_subset_1,dt_c1_1__bvfunc14,dt_c2_1__bvfunc14,dt_c3_1__bvfunc14,dt_c4_1__bvfunc14,dt_c4_1_2__bvfunc14,dt_c5_1_2__bvfunc14,cc1_eqrel_1,cc2_eqrel_1,fc1_subset_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,t1_subset,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole,e13_1_2__bvfunc14,d1_t_1topsp]),
    [interesting(0.65),file(bvfunc14,e14_1_2__bvfunc14),[file(bvfunc14,e14_1_2__bvfunc14)]]).

fof(e15_1_2__bvfunc14,plain,
    ( r2_hidden(c2_1__bvfunc14,c4_1_2__bvfunc14)
    & r2_hidden(c2_1__bvfunc14,c5_1_2__bvfunc14) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_1__bvfunc14,dt_c1_1__bvfunc14,dt_c3_1__bvfunc14,dt_c4_1__bvfunc14])],[dt_k1_xboole_0,fc1_xboole_0,t2_boole,existence_m1_subset_1,dt_m1_subset_1,dt_c1_1__bvfunc14,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t8_boole,commutativity_k3_xboole_0,idempotence_k3_xboole_0,antisymmetry_r2_hidden,dt_k3_xboole_0,dt_c2_1__bvfunc14,dt_c4_1_2__bvfunc14,dt_c5_1_2__bvfunc14,t1_subset,t7_boole,e14_1_2__bvfunc14,d3_xboole_0]),
    [interesting(0.65),file(bvfunc14,e15_1_2__bvfunc14),[file(bvfunc14,e15_1_2__bvfunc14)]]).

fof(e18_1_2__bvfunc14,plain,(
    ~ r1_xboole_0(c5_1_2__bvfunc14,k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,c4_1__bvfunc14)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_1__bvfunc14,dt_c1_1__bvfunc14,dt_c3_1__bvfunc14,dt_c4_1__bvfunc14])],[reflexivity_r1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,fc1_subset_1,fc1_xboole_0,rc1_subset_1,rc2_subset_1,t3_subset,t4_subset,t5_subset,existence_m1_bvfunc_1,existence_m1_eqrel_1,existence_m1_subset_1,redefinition_m1_bvfunc_1,dt_k1_t_1topsp,dt_m1_bvfunc_1,dt_m1_eqrel_1,dt_m1_subset_1,cc1_eqrel_1,cc2_eqrel_1,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t8_boole,symmetry_r1_xboole_0,antisymmetry_r2_hidden,redefinition_k22_bvfunc_1,dt_k22_bvfunc_1,dt_c1_1__bvfunc14,dt_c2_1__bvfunc14,dt_c4_1__bvfunc14,dt_c4_1_2__bvfunc14,dt_c5_1_2__bvfunc14,t1_subset,t7_boole,e9_1_2__bvfunc14,e15_1_2__bvfunc14,t3_xboole_0]),
    [interesting(0.65),file(bvfunc14,e18_1_2__bvfunc14),[file(bvfunc14,e18_1_2__bvfunc14)]]).

fof(d6_eqrel_1,definition,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ( ( A != k1_xboole_0
         => ( m1_eqrel_1(B,A)
          <=> ( k5_setfam_1(A,B) = A
              & ! [C] : 
                  ( m1_subset_1(C,k1_zfmisc_1(A))
                 => ( r2_hidden(C,B)
                   => ( C != k1_xboole_0
                      & ! [D] : 
                          ( m1_subset_1(D,k1_zfmisc_1(A))
                         => ~ ( r2_hidden(D,B)
                              & C != D
                              & ~ r1_xboole_0(C,D) ) ) ) ) ) ) ) )
        & ( A = k1_xboole_0
         => ( m1_eqrel_1(B,A)
          <=> B = k1_xboole_0 ) ) ) ) ),
    file(eqrel_1,d6_eqrel_1),
    [interesting(0.9),axiom,file(eqrel_1,d6_eqrel_1)]).

fof(e19_1_2__bvfunc14,plain,(
    c5_1_2__bvfunc14 = k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,c4_1__bvfunc14) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_1__bvfunc14,dt_c1_1__bvfunc14,dt_c3_1__bvfunc14,dt_c4_1__bvfunc14])],[reflexivity_r1_tarski,existence_m1_bvfunc_1,redefinition_m1_bvfunc_1,dt_k1_t_1topsp,dt_k3_tarski,dt_m1_bvfunc_1,cc1_eqrel_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,t2_subset,t5_subset,t8_boole,commutativity_k2_partit1,commutativity_k3_xboole_0,idempotence_k3_xboole_0,symmetry_r1_xboole_0,antisymmetry_r2_hidden,existence_m1_eqrel_1,existence_m1_subset_1,redefinition_k22_bvfunc_1,redefinition_k5_setfam_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k22_bvfunc_1,dt_k2_partit1,dt_k3_xboole_0,dt_k5_setfam_1,dt_m1_eqrel_1,dt_m1_subset_1,dt_c1_1__bvfunc14,dt_c2_1__bvfunc14,dt_c3_1__bvfunc14,dt_c4_1__bvfunc14,dt_c4_1_2__bvfunc14,dt_c5_1_2__bvfunc14,cc2_eqrel_1,fc1_subset_1,fc1_xboole_0,t1_subset,t2_boole,t3_subset,t4_subset,t6_boole,t7_boole,e18_1_2__bvfunc14,e13_1_2__bvfunc14,d6_eqrel_1]),
    [interesting(0.65),file(bvfunc14,e19_1_2__bvfunc14),[file(bvfunc14,e19_1_2__bvfunc14)]]).

fof(e6_1_2__bvfunc14,plain,(
    ~ r1_xboole_0(k22_bvfunc_1(c1_1__bvfunc14,c2_1_2__bvfunc14,c3_1__bvfunc14),k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,c3_1__bvfunc14)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_1__bvfunc14,dt_c1_1_2__bvfunc14,dt_c2_1__bvfunc14,dt_c4_1__bvfunc14,e1_1_2__bvfunc14,dt_c3_1__bvfunc14])],[reflexivity_r1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,fc1_subset_1,fc1_xboole_0,rc1_subset_1,rc2_subset_1,t3_subset,t4_subset,t5_subset,existence_m1_bvfunc_1,existence_m1_eqrel_1,existence_m1_subset_1,redefinition_m1_bvfunc_1,dt_k1_t_1topsp,dt_m1_bvfunc_1,dt_m1_eqrel_1,dt_m1_subset_1,dt_c1_1_2__bvfunc14,cc1_eqrel_1,cc2_eqrel_1,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t8_boole,symmetry_r1_xboole_0,antisymmetry_r2_hidden,redefinition_k22_bvfunc_1,dt_k22_bvfunc_1,dt_c1_1__bvfunc14,dt_c2_1__bvfunc14,dt_c2_1_2__bvfunc14,dt_c3_1__bvfunc14,dt_c4_1__bvfunc14,de_c2_1_2__bvfunc14,t1_subset,t7_boole,e3_1_2__bvfunc14,e4_1_2__bvfunc14,t3_xboole_0]),
    [interesting(0.65),file(bvfunc14,e6_1_2__bvfunc14),[file(bvfunc14,e6_1_2__bvfunc14)]]).

fof(e8_1_2__bvfunc14,plain,
    ( r2_hidden(c2_1__bvfunc14,k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,c3_1__bvfunc14))
    & r2_hidden(k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,c3_1__bvfunc14),c3_1__bvfunc14) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_1__bvfunc14,dt_c2_1__bvfunc14,dt_c3_1__bvfunc14])],[reflexivity_r1_tarski,existence_m1_bvfunc_1,redefinition_m1_bvfunc_1,dt_k1_xboole_0,dt_m1_bvfunc_1,fc1_xboole_0,antisymmetry_r2_hidden,existence_m1_eqrel_1,existence_m1_subset_1,redefinition_k22_bvfunc_1,dt_k1_t_1topsp,dt_k1_zfmisc_1,dt_k22_bvfunc_1,dt_m1_eqrel_1,dt_m1_subset_1,dt_c1_1__bvfunc14,dt_c2_1__bvfunc14,dt_c3_1__bvfunc14,cc1_eqrel_1,cc2_eqrel_1,fc1_subset_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,t1_subset,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole,d1_t_1topsp]),
    [interesting(0.65),file(bvfunc14,e8_1_2__bvfunc14),[file(bvfunc14,e8_1_2__bvfunc14)]]).

fof(e16_1_2__bvfunc14,plain,(
    ~ r1_xboole_0(c4_1_2__bvfunc14,k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,c3_1__bvfunc14)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c4_1__bvfunc14,dt_c1_1__bvfunc14,dt_c2_1__bvfunc14,dt_c3_1__bvfunc14])],[reflexivity_r1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,fc1_subset_1,fc1_xboole_0,rc1_subset_1,rc2_subset_1,t3_subset,t4_subset,t5_subset,existence_m1_bvfunc_1,existence_m1_eqrel_1,existence_m1_subset_1,redefinition_m1_bvfunc_1,dt_k1_t_1topsp,dt_m1_bvfunc_1,dt_m1_eqrel_1,dt_m1_subset_1,cc1_eqrel_1,cc2_eqrel_1,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t8_boole,symmetry_r1_xboole_0,antisymmetry_r2_hidden,redefinition_k22_bvfunc_1,dt_k22_bvfunc_1,dt_c1_1__bvfunc14,dt_c2_1__bvfunc14,dt_c3_1__bvfunc14,dt_c4_1_2__bvfunc14,dt_c5_1_2__bvfunc14,t1_subset,t7_boole,e15_1_2__bvfunc14,e8_1_2__bvfunc14,t3_xboole_0]),
    [interesting(0.65),file(bvfunc14,e16_1_2__bvfunc14),[file(bvfunc14,e16_1_2__bvfunc14)]]).

fof(e17_1_2__bvfunc14,plain,(
    c4_1_2__bvfunc14 = k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,c3_1__bvfunc14) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_1__bvfunc14,dt_c1_1__bvfunc14,dt_c3_1__bvfunc14,dt_c4_1__bvfunc14])],[reflexivity_r1_tarski,existence_m1_bvfunc_1,redefinition_m1_bvfunc_1,dt_k1_t_1topsp,dt_k3_tarski,dt_m1_bvfunc_1,cc1_eqrel_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,t2_subset,t5_subset,t8_boole,commutativity_k2_partit1,commutativity_k3_xboole_0,idempotence_k3_xboole_0,symmetry_r1_xboole_0,antisymmetry_r2_hidden,existence_m1_eqrel_1,existence_m1_subset_1,redefinition_k22_bvfunc_1,redefinition_k5_setfam_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k22_bvfunc_1,dt_k2_partit1,dt_k3_xboole_0,dt_k5_setfam_1,dt_m1_eqrel_1,dt_m1_subset_1,dt_c1_1__bvfunc14,dt_c2_1__bvfunc14,dt_c3_1__bvfunc14,dt_c4_1__bvfunc14,dt_c4_1_2__bvfunc14,dt_c5_1_2__bvfunc14,cc2_eqrel_1,fc1_subset_1,fc1_xboole_0,t1_subset,t2_boole,t3_subset,t4_subset,t6_boole,t7_boole,e16_1_2__bvfunc14,e13_1_2__bvfunc14,d6_eqrel_1]),
    [interesting(0.65),file(bvfunc14,e17_1_2__bvfunc14),[file(bvfunc14,e17_1_2__bvfunc14)]]).

fof(t9_t_1topsp,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_eqrel_1(B,A)
         => ! [C] : 
              ( m1_subset_1(C,A)
             => ! [D] : 
                  ( m1_subset_1(D,A)
                 => ( ~ r1_xboole_0(k1_t_1topsp(A,C,B),k1_t_1topsp(A,D,B))
                   => k1_t_1topsp(A,C,B) = k1_t_1topsp(A,D,B) ) ) ) ) ) ),
    file(t_1topsp,t9_t_1topsp),
    [interesting(0.9),axiom,file(t_1topsp,t9_t_1topsp)]).

fof(e20_1_2__bvfunc14,plain,(
    c4_1_2__bvfunc14 = k22_bvfunc_1(c1_1__bvfunc14,c2_1_2__bvfunc14,c3_1__bvfunc14) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_1_2__bvfunc14,e1_1_2__bvfunc14,dt_c2_1__bvfunc14,dt_c1_1__bvfunc14,dt_c3_1__bvfunc14,dt_c4_1__bvfunc14])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_m1_bvfunc_1,redefinition_m1_bvfunc_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_m1_bvfunc_1,dt_c1_1_2__bvfunc14,fc1_subset_1,fc1_xboole_0,rc1_subset_1,rc2_subset_1,t1_subset,t3_subset,t4_subset,t5_subset,symmetry_r1_xboole_0,existence_m1_eqrel_1,existence_m1_subset_1,redefinition_k22_bvfunc_1,dt_k1_t_1topsp,dt_k22_bvfunc_1,dt_m1_eqrel_1,dt_m1_subset_1,dt_c1_1__bvfunc14,dt_c2_1__bvfunc14,dt_c2_1_2__bvfunc14,dt_c3_1__bvfunc14,dt_c4_1_2__bvfunc14,de_c2_1_2__bvfunc14,cc1_eqrel_1,cc2_eqrel_1,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t7_boole,t8_boole,e6_1_2__bvfunc14,e17_1_2__bvfunc14,t9_t_1topsp]),
    [interesting(0.65),file(bvfunc14,e20_1_2__bvfunc14),[file(bvfunc14,e20_1_2__bvfunc14)]]).

fof(e22_1_2__bvfunc14,plain,(
    r2_hidden(c1_1_2__bvfunc14,k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,k2_partit1(c1_1__bvfunc14,c3_1__bvfunc14,c4_1__bvfunc14))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_1_2__bvfunc14,e1_1_2__bvfunc14,dt_c2_1__bvfunc14,dt_c1_1__bvfunc14,dt_c3_1__bvfunc14,dt_c4_1__bvfunc14])],[reflexivity_r1_tarski,existence_m1_bvfunc_1,redefinition_m1_bvfunc_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_m1_bvfunc_1,fc1_subset_1,fc1_xboole_0,rc1_subset_1,rc2_subset_1,t2_boole,t3_subset,t4_subset,t5_subset,commutativity_k2_partit1,commutativity_k3_xboole_0,idempotence_k3_xboole_0,commutativity_k5_subset_1,idempotence_k5_subset_1,symmetry_r1_xboole_0,antisymmetry_r2_hidden,existence_m1_eqrel_1,existence_m1_subset_1,redefinition_k22_bvfunc_1,redefinition_k5_subset_1,dt_k1_t_1topsp,dt_k22_bvfunc_1,dt_k2_partit1,dt_k3_xboole_0,dt_k5_subset_1,dt_m1_eqrel_1,dt_m1_subset_1,dt_c1_1__bvfunc14,dt_c1_1_2__bvfunc14,dt_c2_1__bvfunc14,dt_c2_1_2__bvfunc14,dt_c3_1__bvfunc14,dt_c4_1__bvfunc14,dt_c4_1_2__bvfunc14,dt_c5_1_2__bvfunc14,de_c2_1_2__bvfunc14,cc1_eqrel_1,cc2_eqrel_1,rc1_xboole_0,rc2_xboole_0,t1_subset,t2_subset,t6_boole,t7_boole,t8_boole,e21_1_2__bvfunc14,e7_1_2__bvfunc14,e13_1_2__bvfunc14,e19_1_2__bvfunc14,e20_1_2__bvfunc14,t9_t_1topsp]),
    [interesting(0.65),file(bvfunc14,e22_1_2__bvfunc14),[file(bvfunc14,e22_1_2__bvfunc14)]]).

fof(i3_1_2__bvfunc14,theorem,(
    $true ),
    introduced(tautology,[file(bvfunc14,i3_1_2__bvfunc14)]),
    [interesting(0.65),trivial,file(bvfunc14,i3_1_2__bvfunc14)]).

fof(i2_1_2__bvfunc14,plain,(
    r2_hidden(c1_1_2__bvfunc14,k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,k2_partit1(c1_1__bvfunc14,c3_1__bvfunc14,c4_1__bvfunc14))) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_1_2__bvfunc14,e1_1_2__bvfunc14,dt_c2_1__bvfunc14,dt_c1_1__bvfunc14,dt_c3_1__bvfunc14,dt_c4_1__bvfunc14])],[e22_1_2__bvfunc14,i3_1_2__bvfunc14]),
    [interesting(0.65),file(bvfunc14,i2_1_2__bvfunc14),[file(bvfunc14,i2_1_2__bvfunc14)]]).

fof(i1_1_2__bvfunc14,plain,(
    ~ ( r2_hidden(c1_1_2__bvfunc14,k5_subset_1(c1_1__bvfunc14,k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,c3_1__bvfunc14),k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,c4_1__bvfunc14)))
      & ~ r2_hidden(c1_1_2__bvfunc14,k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,k2_partit1(c1_1__bvfunc14,c3_1__bvfunc14,c4_1__bvfunc14))) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_1_2__bvfunc14,dt_c2_1__bvfunc14,dt_c1_1__bvfunc14,dt_c3_1__bvfunc14,dt_c4_1__bvfunc14]),discharge_asm(discharge,[e1_1_2__bvfunc14])],[e1_1_2__bvfunc14,i2_1_2__bvfunc14]),
    [interesting(0.65),file(bvfunc14,i1_1_2__bvfunc14),[file(bvfunc14,i1_1_2__bvfunc14)]]).

fof(i1_1_2_tmp__bvfunc14,plain,(
    ~ ( r2_hidden(c1_1_2__bvfunc14,k5_subset_1(c1_1__bvfunc14,k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,c3_1__bvfunc14),k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,c4_1__bvfunc14)))
      & ~ r2_hidden(c1_1_2__bvfunc14,k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,k2_partit1(c1_1__bvfunc14,c3_1__bvfunc14,c4_1__bvfunc14))) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c2_1__bvfunc14,dt_c1_1__bvfunc14,dt_c3_1__bvfunc14,dt_c4_1__bvfunc14]),discharge_asm(discharge,[dt_c1_1_2__bvfunc14])],[dt_c1_1_2__bvfunc14,i1_1_2__bvfunc14]),
    [interesting(0.8),e2_1__bvfunc14]).

fof(e2_1__bvfunc14,plain,(
    r1_tarski(k5_subset_1(c1_1__bvfunc14,k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,c3_1__bvfunc14),k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,c4_1__bvfunc14)),k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,k2_partit1(c1_1__bvfunc14,c3_1__bvfunc14,c4_1__bvfunc14))) ),
    inference(let,[status(thm),assumptions([dt_c2_1__bvfunc14,dt_c1_1__bvfunc14,dt_c3_1__bvfunc14,dt_c4_1__bvfunc14])],[i1_1_2_tmp__bvfunc14,commutativity_k3_xboole_0,idempotence_k3_xboole_0,redefinition_m1_bvfunc_1,dt_k1_t_1topsp,dt_k1_zfmisc_1,dt_k3_xboole_0,dt_m1_bvfunc_1,dt_m1_eqrel_1,dt_m1_subset_1,cc1_eqrel_1,cc2_eqrel_1,fc1_subset_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,commutativity_k2_partit1,commutativity_k5_subset_1,idempotence_k5_subset_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,redefinition_k22_bvfunc_1,redefinition_k5_subset_1,dt_k22_bvfunc_1,dt_k2_partit1,dt_k5_subset_1,dt_c1_1__bvfunc14,dt_c2_1__bvfunc14,dt_c3_1__bvfunc14,dt_c4_1__bvfunc14,d3_tarski,dh_c1_1_2__bvfunc14]),
    [interesting(0.8),file(bvfunc14,e2_1__bvfunc14),[file(bvfunc14,e2_1__bvfunc14)]]).

fof(dt_c1_1_1__bvfunc14,assumption,(
    $true ),
    introduced(assumption,[file(bvfunc14,c1_1_1__bvfunc14)]),
    [interesting(0.65),axiom,file(bvfunc14,c1_1_1__bvfunc14)]).

fof(dh_c1_1_1__bvfunc14,definition,
    ( ~ ( r2_hidden(c1_1_1__bvfunc14,k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,k2_partit1(c1_1__bvfunc14,c3_1__bvfunc14,c4_1__bvfunc14)))
        & ~ r2_hidden(c1_1_1__bvfunc14,k5_subset_1(c1_1__bvfunc14,k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,c3_1__bvfunc14),k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,c4_1__bvfunc14))) )
   => ! [A] : 
        ~ ( r2_hidden(A,k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,k2_partit1(c1_1__bvfunc14,c3_1__bvfunc14,c4_1__bvfunc14)))
          & ~ r2_hidden(A,k5_subset_1(c1_1__bvfunc14,k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,c3_1__bvfunc14),k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,c4_1__bvfunc14))) ) ),
    introduced(definition,[new_symbol(c1_1_1__bvfunc14),file(bvfunc14,c1_1_1__bvfunc14)]),
    [interesting(0.65),axiom,file(bvfunc14,c1_1_1__bvfunc14)]).

fof(e1_1_1__bvfunc14,assumption,(
    r2_hidden(c1_1_1__bvfunc14,k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,k2_partit1(c1_1__bvfunc14,c3_1__bvfunc14,c4_1__bvfunc14))) ),
    introduced(assumption,[file(bvfunc14,e1_1_1__bvfunc14)]),
    [interesting(0.65),axiom,file(bvfunc14,e1_1_1__bvfunc14)]).

fof(t3_bvfunc11,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ! [C] : 
              ( m1_eqrel_1(C,A)
             => ! [D] : 
                  ( m1_eqrel_1(D,A)
                 => r1_tarski(k22_bvfunc_1(A,B,k2_partit1(A,C,D)),k22_bvfunc_1(A,B,C)) ) ) ) ) ),
    file(bvfunc11,t3_bvfunc11),
    [interesting(0.9),axiom,file(bvfunc11,t3_bvfunc11)]).

fof(e3_1_1__bvfunc14,plain,(
    r1_tarski(k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,k2_partit1(c1_1__bvfunc14,c3_1__bvfunc14,c4_1__bvfunc14)),k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,c4_1__bvfunc14)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_1__bvfunc14,dt_c2_1__bvfunc14,dt_c3_1__bvfunc14,dt_c4_1__bvfunc14])],[antisymmetry_r2_hidden,existence_m1_bvfunc_1,redefinition_m1_bvfunc_1,dt_k1_t_1topsp,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_m1_bvfunc_1,fc1_subset_1,fc1_xboole_0,rc1_subset_1,rc2_subset_1,t1_subset,t4_subset,t5_subset,t8_boole,commutativity_k2_partit1,reflexivity_r1_tarski,existence_m1_eqrel_1,existence_m1_subset_1,redefinition_k22_bvfunc_1,dt_k22_bvfunc_1,dt_k2_partit1,dt_m1_eqrel_1,dt_m1_subset_1,dt_c1_1__bvfunc14,dt_c2_1__bvfunc14,dt_c3_1__bvfunc14,dt_c4_1__bvfunc14,cc1_eqrel_1,cc2_eqrel_1,rc1_xboole_0,rc2_xboole_0,t2_subset,t3_subset,t6_boole,t7_boole,t3_bvfunc11]),
    [interesting(0.65),file(bvfunc14,e3_1_1__bvfunc14),[file(bvfunc14,e3_1_1__bvfunc14)]]).

fof(e2_1_1__bvfunc14,plain,(
    r1_tarski(k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,k2_partit1(c1_1__bvfunc14,c3_1__bvfunc14,c4_1__bvfunc14)),k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,c3_1__bvfunc14)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_1__bvfunc14,dt_c2_1__bvfunc14,dt_c3_1__bvfunc14,dt_c4_1__bvfunc14])],[antisymmetry_r2_hidden,existence_m1_bvfunc_1,redefinition_m1_bvfunc_1,dt_k1_t_1topsp,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_m1_bvfunc_1,fc1_subset_1,fc1_xboole_0,rc1_subset_1,rc2_subset_1,t1_subset,t4_subset,t5_subset,t8_boole,commutativity_k2_partit1,reflexivity_r1_tarski,existence_m1_eqrel_1,existence_m1_subset_1,redefinition_k22_bvfunc_1,dt_k22_bvfunc_1,dt_k2_partit1,dt_m1_eqrel_1,dt_m1_subset_1,dt_c1_1__bvfunc14,dt_c2_1__bvfunc14,dt_c3_1__bvfunc14,dt_c4_1__bvfunc14,cc1_eqrel_1,cc2_eqrel_1,rc1_xboole_0,rc2_xboole_0,t2_subset,t3_subset,t6_boole,t7_boole,t3_bvfunc11]),
    [interesting(0.65),file(bvfunc14,e2_1_1__bvfunc14),[file(bvfunc14,e2_1_1__bvfunc14)]]).

fof(e4_1_1__bvfunc14,plain,(
    r2_hidden(c1_1_1__bvfunc14,k5_subset_1(c1_1__bvfunc14,k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,c3_1__bvfunc14),k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,c4_1__bvfunc14))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_1_1__bvfunc14,e1_1_1__bvfunc14,dt_c1_1__bvfunc14,dt_c2_1__bvfunc14,dt_c3_1__bvfunc14,dt_c4_1__bvfunc14])],[dt_k1_xboole_0,fc1_xboole_0,t2_boole,existence_m1_bvfunc_1,existence_m1_eqrel_1,existence_m1_subset_1,redefinition_m1_bvfunc_1,dt_k1_t_1topsp,dt_k1_zfmisc_1,dt_m1_bvfunc_1,dt_m1_eqrel_1,dt_m1_subset_1,cc1_eqrel_1,cc2_eqrel_1,fc1_subset_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,t2_subset,t4_subset,t5_subset,t6_boole,t8_boole,commutativity_k2_partit1,commutativity_k3_xboole_0,idempotence_k3_xboole_0,commutativity_k5_subset_1,idempotence_k5_subset_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,redefinition_k22_bvfunc_1,redefinition_k5_subset_1,dt_k22_bvfunc_1,dt_k2_partit1,dt_k3_xboole_0,dt_k5_subset_1,dt_c1_1__bvfunc14,dt_c1_1_1__bvfunc14,dt_c2_1__bvfunc14,dt_c3_1__bvfunc14,dt_c4_1__bvfunc14,t1_subset,t3_subset,t7_boole,e3_1_1__bvfunc14,e1_1_1__bvfunc14,e2_1_1__bvfunc14,d3_xboole_0]),
    [interesting(0.65),file(bvfunc14,e4_1_1__bvfunc14),[file(bvfunc14,e4_1_1__bvfunc14)]]).

fof(i3_1_1__bvfunc14,theorem,(
    $true ),
    introduced(tautology,[file(bvfunc14,i3_1_1__bvfunc14)]),
    [interesting(0.65),trivial,file(bvfunc14,i3_1_1__bvfunc14)]).

fof(i2_1_1__bvfunc14,plain,(
    r2_hidden(c1_1_1__bvfunc14,k5_subset_1(c1_1__bvfunc14,k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,c3_1__bvfunc14),k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,c4_1__bvfunc14))) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_1_1__bvfunc14,e1_1_1__bvfunc14,dt_c1_1__bvfunc14,dt_c2_1__bvfunc14,dt_c3_1__bvfunc14,dt_c4_1__bvfunc14])],[e4_1_1__bvfunc14,i3_1_1__bvfunc14]),
    [interesting(0.65),file(bvfunc14,i2_1_1__bvfunc14),[file(bvfunc14,i2_1_1__bvfunc14)]]).

fof(i1_1_1__bvfunc14,plain,(
    ~ ( r2_hidden(c1_1_1__bvfunc14,k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,k2_partit1(c1_1__bvfunc14,c3_1__bvfunc14,c4_1__bvfunc14)))
      & ~ r2_hidden(c1_1_1__bvfunc14,k5_subset_1(c1_1__bvfunc14,k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,c3_1__bvfunc14),k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,c4_1__bvfunc14))) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_1_1__bvfunc14,dt_c1_1__bvfunc14,dt_c2_1__bvfunc14,dt_c3_1__bvfunc14,dt_c4_1__bvfunc14]),discharge_asm(discharge,[e1_1_1__bvfunc14])],[e1_1_1__bvfunc14,i2_1_1__bvfunc14]),
    [interesting(0.65),file(bvfunc14,i1_1_1__bvfunc14),[file(bvfunc14,i1_1_1__bvfunc14)]]).

fof(i1_1_1_tmp__bvfunc14,plain,(
    ~ ( r2_hidden(c1_1_1__bvfunc14,k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,k2_partit1(c1_1__bvfunc14,c3_1__bvfunc14,c4_1__bvfunc14)))
      & ~ r2_hidden(c1_1_1__bvfunc14,k5_subset_1(c1_1__bvfunc14,k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,c3_1__bvfunc14),k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,c4_1__bvfunc14))) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_1__bvfunc14,dt_c2_1__bvfunc14,dt_c3_1__bvfunc14,dt_c4_1__bvfunc14]),discharge_asm(discharge,[dt_c1_1_1__bvfunc14])],[dt_c1_1_1__bvfunc14,i1_1_1__bvfunc14]),
    [interesting(0.8),e1_1__bvfunc14]).

fof(e1_1__bvfunc14,plain,(
    r1_tarski(k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,k2_partit1(c1_1__bvfunc14,c3_1__bvfunc14,c4_1__bvfunc14)),k5_subset_1(c1_1__bvfunc14,k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,c3_1__bvfunc14),k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,c4_1__bvfunc14))) ),
    inference(let,[status(thm),assumptions([dt_c1_1__bvfunc14,dt_c2_1__bvfunc14,dt_c3_1__bvfunc14,dt_c4_1__bvfunc14])],[i1_1_1_tmp__bvfunc14,commutativity_k3_xboole_0,idempotence_k3_xboole_0,redefinition_m1_bvfunc_1,dt_k1_t_1topsp,dt_k1_zfmisc_1,dt_k3_xboole_0,dt_m1_bvfunc_1,dt_m1_eqrel_1,dt_m1_subset_1,cc1_eqrel_1,cc2_eqrel_1,fc1_subset_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,commutativity_k2_partit1,commutativity_k5_subset_1,idempotence_k5_subset_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,redefinition_k22_bvfunc_1,redefinition_k5_subset_1,dt_k22_bvfunc_1,dt_k2_partit1,dt_k5_subset_1,dt_c1_1__bvfunc14,dt_c2_1__bvfunc14,dt_c3_1__bvfunc14,dt_c4_1__bvfunc14,d3_tarski,dh_c1_1_1__bvfunc14]),
    [interesting(0.8),file(bvfunc14,e1_1__bvfunc14),[file(bvfunc14,e1_1__bvfunc14)]]).

fof(d10_xboole_0,definition,(
    ! [A,B] : 
      ( A = B
    <=> ( r1_tarski(A,B)
        & r1_tarski(B,A) ) ) ),
    file(xboole_0,d10_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,d10_xboole_0)]).

fof(e3_1__bvfunc14,plain,(
    k5_subset_1(c1_1__bvfunc14,k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,c3_1__bvfunc14),k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,c4_1__bvfunc14)) = k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,k2_partit1(c1_1__bvfunc14,c3_1__bvfunc14,c4_1__bvfunc14)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_1__bvfunc14,dt_c2_1__bvfunc14,dt_c3_1__bvfunc14,dt_c4_1__bvfunc14])],[antisymmetry_r2_hidden,dt_k1_xboole_0,fc1_xboole_0,t1_subset,t2_boole,t4_subset,t5_subset,commutativity_k3_xboole_0,idempotence_k3_xboole_0,existence_m1_bvfunc_1,existence_m1_eqrel_1,existence_m1_subset_1,redefinition_m1_bvfunc_1,dt_k1_t_1topsp,dt_k1_zfmisc_1,dt_k3_xboole_0,dt_m1_bvfunc_1,dt_m1_eqrel_1,dt_m1_subset_1,cc1_eqrel_1,cc2_eqrel_1,fc1_subset_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k2_partit1,commutativity_k5_subset_1,idempotence_k5_subset_1,reflexivity_r1_tarski,redefinition_k22_bvfunc_1,redefinition_k5_subset_1,dt_k22_bvfunc_1,dt_k2_partit1,dt_k5_subset_1,dt_c1_1__bvfunc14,dt_c2_1__bvfunc14,dt_c3_1__bvfunc14,dt_c4_1__bvfunc14,t3_subset,e2_1__bvfunc14,e1_1__bvfunc14,d10_xboole_0]),
    [interesting(0.8),file(bvfunc14,e3_1__bvfunc14),[file(bvfunc14,e3_1__bvfunc14)]]).

fof(i4_1__bvfunc14,theorem,(
    $true ),
    introduced(tautology,[file(bvfunc14,i4_1__bvfunc14)]),
    [interesting(0.8),trivial,file(bvfunc14,i4_1__bvfunc14)]).

fof(i3_1__bvfunc14,plain,(
    k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,k2_partit1(c1_1__bvfunc14,c3_1__bvfunc14,c4_1__bvfunc14)) = k5_subset_1(c1_1__bvfunc14,k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,c3_1__bvfunc14),k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,c4_1__bvfunc14)) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_1__bvfunc14,dt_c2_1__bvfunc14,dt_c3_1__bvfunc14,dt_c4_1__bvfunc14])],[e3_1__bvfunc14,i4_1__bvfunc14]),
    [interesting(0.8),file(bvfunc14,i3_1__bvfunc14),[file(bvfunc14,i3_1__bvfunc14)]]).

fof(i3_1_tmp__bvfunc14,plain,
    ( ( m1_eqrel_1(c3_1__bvfunc14,c1_1__bvfunc14)
      & m1_eqrel_1(c4_1__bvfunc14,c1_1__bvfunc14) )
   => k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,k2_partit1(c1_1__bvfunc14,c3_1__bvfunc14,c4_1__bvfunc14)) = k5_subset_1(c1_1__bvfunc14,k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,c3_1__bvfunc14),k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,c4_1__bvfunc14)) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_1__bvfunc14,dt_c2_1__bvfunc14]),discharge_asm(discharge,[dt_c3_1__bvfunc14,dt_c4_1__bvfunc14])],[dt_c3_1__bvfunc14,dt_c4_1__bvfunc14,i3_1__bvfunc14]),
    [interesting(0.8),i2_1__bvfunc14]).

fof(i2_1__bvfunc14,plain,(
    ! [A] : 
      ( m1_eqrel_1(A,c1_1__bvfunc14)
     => ! [B] : 
          ( m1_eqrel_1(B,c1_1__bvfunc14)
         => k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,k2_partit1(c1_1__bvfunc14,A,B)) = k5_subset_1(c1_1__bvfunc14,k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,A),k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,B)) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_1__bvfunc14,dt_c2_1__bvfunc14])],[i3_1_tmp__bvfunc14,dh_c3_1__bvfunc14,dh_c4_1__bvfunc14]),
    [interesting(0.8),file(bvfunc14,i2_1__bvfunc14),[file(bvfunc14,i2_1__bvfunc14)]]).

fof(i2_1_tmp__bvfunc14,plain,
    ( m1_subset_1(c2_1__bvfunc14,c1_1__bvfunc14)
   => ! [A] : 
        ( m1_eqrel_1(A,c1_1__bvfunc14)
       => ! [B] : 
            ( m1_eqrel_1(B,c1_1__bvfunc14)
           => k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,k2_partit1(c1_1__bvfunc14,A,B)) = k5_subset_1(c1_1__bvfunc14,k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,A),k22_bvfunc_1(c1_1__bvfunc14,c2_1__bvfunc14,B)) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_1__bvfunc14]),discharge_asm(discharge,[dt_c2_1__bvfunc14])],[dt_c2_1__bvfunc14,i2_1__bvfunc14]),
    [interesting(0.8),i1_1__bvfunc14]).

fof(i1_1__bvfunc14,plain,(
    ! [A] : 
      ( m1_subset_1(A,c1_1__bvfunc14)
     => ! [B] : 
          ( m1_eqrel_1(B,c1_1__bvfunc14)
         => ! [C] : 
              ( m1_eqrel_1(C,c1_1__bvfunc14)
             => k22_bvfunc_1(c1_1__bvfunc14,A,k2_partit1(c1_1__bvfunc14,B,C)) = k5_subset_1(c1_1__bvfunc14,k22_bvfunc_1(c1_1__bvfunc14,A,B),k22_bvfunc_1(c1_1__bvfunc14,A,C)) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_1__bvfunc14])],[i2_1_tmp__bvfunc14,dh_c2_1__bvfunc14]),
    [interesting(0.8),file(bvfunc14,i1_1__bvfunc14),[file(bvfunc14,i1_1__bvfunc14)]]).

fof(i1_1_tmp__bvfunc14,plain,
    ( ~ v1_xboole_0(c1_1__bvfunc14)
   => ! [A] : 
        ( m1_subset_1(A,c1_1__bvfunc14)
       => ! [B] : 
            ( m1_eqrel_1(B,c1_1__bvfunc14)
           => ! [C] : 
                ( m1_eqrel_1(C,c1_1__bvfunc14)
               => k22_bvfunc_1(c1_1__bvfunc14,A,k2_partit1(c1_1__bvfunc14,B,C)) = k5_subset_1(c1_1__bvfunc14,k22_bvfunc_1(c1_1__bvfunc14,A,B),k22_bvfunc_1(c1_1__bvfunc14,A,C)) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_1__bvfunc14])],[dt_c1_1__bvfunc14,i1_1__bvfunc14]),
    [interesting(1),t1_bvfunc14]).

fof(t1_bvfunc14,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ! [C] : 
              ( m1_eqrel_1(C,A)
             => ! [D] : 
                  ( m1_eqrel_1(D,A)
                 => k22_bvfunc_1(A,B,k2_partit1(A,C,D)) = k5_subset_1(A,k22_bvfunc_1(A,B,C),k22_bvfunc_1(A,B,D)) ) ) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_1_tmp__bvfunc14,dh_c1_1__bvfunc14]),
    [interesting(1),file(bvfunc14,t1_bvfunc14),[file(bvfunc14,t1_bvfunc14)]]).