% Mizar ND problem: t7_bvfunc11,bvfunc11,197,13 
fof(dh_c1_7__bvfunc11,definition,
    ( ( ~ v1_xboole_0(c1_7__bvfunc11)
     => ! [A] : 
          ( m1_subset_1(A,k1_zfmisc_1(k1_bvfunc_2(c1_7__bvfunc11)))
         => ! [B] : 
              ( m1_eqrel_1(B,c1_7__bvfunc11)
             => ! [C] : 
                  ( m1_eqrel_1(C,c1_7__bvfunc11)
                 => ( A = k2_tarski(B,C)
                   => ( B = C
                      | k5_bvfunc_2(c1_7__bvfunc11,B,A) = C ) ) ) ) ) )
   => ! [D] : 
        ( ~ v1_xboole_0(D)
       => ! [E] : 
            ( m1_subset_1(E,k1_zfmisc_1(k1_bvfunc_2(D)))
           => ! [F] : 
                ( m1_eqrel_1(F,D)
               => ! [G] : 
                    ( m1_eqrel_1(G,D)
                   => ( E = k2_tarski(F,G)
                     => ( F = G
                        | k5_bvfunc_2(D,F,E) = G ) ) ) ) ) ) ),
    introduced(definition,[new_symbol(c1_7__bvfunc11),file(bvfunc11,c1_7__bvfunc11)]),
    [interesting(0.8),axiom,file(bvfunc11,c1_7__bvfunc11)]).

fof(dh_c2_7__bvfunc11,definition,
    ( ( m1_subset_1(c2_7__bvfunc11,k1_zfmisc_1(k1_bvfunc_2(c1_7__bvfunc11)))
     => ! [A] : 
          ( m1_eqrel_1(A,c1_7__bvfunc11)
         => ! [B] : 
              ( m1_eqrel_1(B,c1_7__bvfunc11)
             => ( c2_7__bvfunc11 = k2_tarski(A,B)
               => ( A = B
                  | k5_bvfunc_2(c1_7__bvfunc11,A,c2_7__bvfunc11) = B ) ) ) ) )
   => ! [C] : 
        ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(c1_7__bvfunc11)))
       => ! [D] : 
            ( m1_eqrel_1(D,c1_7__bvfunc11)
           => ! [E] : 
                ( m1_eqrel_1(E,c1_7__bvfunc11)
               => ( C = k2_tarski(D,E)
                 => ( D = E
                    | k5_bvfunc_2(c1_7__bvfunc11,D,C) = E ) ) ) ) ) ),
    introduced(definition,[new_symbol(c2_7__bvfunc11),file(bvfunc11,c2_7__bvfunc11)]),
    [interesting(0.8),axiom,file(bvfunc11,c2_7__bvfunc11)]).

fof(dh_c3_7__bvfunc11,definition,
    ( ( m1_eqrel_1(c3_7__bvfunc11,c1_7__bvfunc11)
     => ! [A] : 
          ( m1_eqrel_1(A,c1_7__bvfunc11)
         => ( c2_7__bvfunc11 = k2_tarski(c3_7__bvfunc11,A)
           => ( c3_7__bvfunc11 = A
              | k5_bvfunc_2(c1_7__bvfunc11,c3_7__bvfunc11,c2_7__bvfunc11) = A ) ) ) )
   => ! [B] : 
        ( m1_eqrel_1(B,c1_7__bvfunc11)
       => ! [C] : 
            ( m1_eqrel_1(C,c1_7__bvfunc11)
           => ( c2_7__bvfunc11 = k2_tarski(B,C)
             => ( B = C
                | k5_bvfunc_2(c1_7__bvfunc11,B,c2_7__bvfunc11) = C ) ) ) ) ),
    introduced(definition,[new_symbol(c3_7__bvfunc11),file(bvfunc11,c3_7__bvfunc11)]),
    [interesting(0.8),axiom,file(bvfunc11,c3_7__bvfunc11)]).

fof(dh_c4_7__bvfunc11,definition,
    ( ( m1_eqrel_1(c4_7__bvfunc11,c1_7__bvfunc11)
     => ( c2_7__bvfunc11 = k2_tarski(c3_7__bvfunc11,c4_7__bvfunc11)
       => ( c3_7__bvfunc11 = c4_7__bvfunc11
          | k5_bvfunc_2(c1_7__bvfunc11,c3_7__bvfunc11,c2_7__bvfunc11) = c4_7__bvfunc11 ) ) )
   => ! [A] : 
        ( m1_eqrel_1(A,c1_7__bvfunc11)
       => ( c2_7__bvfunc11 = k2_tarski(c3_7__bvfunc11,A)
         => ( c3_7__bvfunc11 = A
            | k5_bvfunc_2(c1_7__bvfunc11,c3_7__bvfunc11,c2_7__bvfunc11) = A ) ) ) ),
    introduced(definition,[new_symbol(c4_7__bvfunc11),file(bvfunc11,c4_7__bvfunc11)]),
    [interesting(0.8),axiom,file(bvfunc11,c4_7__bvfunc11)]).

fof(e1_7__bvfunc11,assumption,
    ( c2_7__bvfunc11 = k2_tarski(c3_7__bvfunc11,c4_7__bvfunc11)
    & c3_7__bvfunc11 != c4_7__bvfunc11 ),
    introduced(assumption,[file(bvfunc11,e1_7__bvfunc11)]),
    [interesting(0.8),axiom,file(bvfunc11,e1_7__bvfunc11)]).

fof(cc1_funct_7,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A)
        & v1_funct_7(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finset_1(A)
        & v1_finseq_1(A)
        & v1_funcop_1(A) ) ) ),
    file(funct_7,cc1_funct_7),
    [interesting(0.9),axiom,file(funct_7,cc1_funct_7)]).

fof(cc2_funct_7,theorem,(
    ! [A] : 
      ( ( v1_xboole_0(A)
        & v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finset_1(A)
        & v1_finseq_1(A)
        & v1_funcop_1(A)
        & v1_funct_7(A) ) ) ),
    file(funct_7,cc2_funct_7),
    [interesting(0.9),axiom,file(funct_7,cc2_funct_7)]).

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

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(existence_m1_t_1topsp,axiom,(
    ! [A] : 
    ? [B] : m1_t_1topsp(B,A) ),
    file(t_1topsp,m1_t_1topsp),
    [interesting(0.9),axiom,file(t_1topsp,m1_t_1topsp)]).

fof(dt_k1_partit1,axiom,(
    $true ),
    file(partit1,k1_partit1),
    [interesting(0.9),axiom,file(partit1,k1_partit1)]).

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

fof(dt_m1_t_1topsp,axiom,(
    $true ),
    file(t_1topsp,m1_t_1topsp),
    [interesting(0.9),axiom,file(t_1topsp,m1_t_1topsp)]).

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

fof(fc3_funct_7,theorem,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0)
    & v3_relat_1(k1_xboole_0)
    & v1_funct_1(k1_xboole_0)
    & v2_funct_1(k1_xboole_0)
    & v1_finset_1(k1_xboole_0)
    & v1_finseq_1(k1_xboole_0)
    & v1_funcop_1(k1_xboole_0) ),
    file(funct_7,fc3_funct_7),
    [interesting(0.9),axiom,file(funct_7,fc3_funct_7)]).

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(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(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_k1_bvfunc_2,definition,(
    ! [A] : k1_bvfunc_2(A) = k1_partit1(A) ),
    file(bvfunc_2,k1_bvfunc_2),
    [interesting(0.9),axiom,file(bvfunc_2,k1_bvfunc_2)]).

fof(dt_k1_bvfunc_2,axiom,(
    ! [A] : 
      ( v1_t_1topsp(k1_bvfunc_2(A),A)
      & m1_t_1topsp(k1_bvfunc_2(A),A) ) ),
    file(bvfunc_2,k1_bvfunc_2),
    [interesting(0.9),axiom,file(bvfunc_2,k1_bvfunc_2)]).

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

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

fof(redefinition_k4_bvfunc_2,definition,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_eqrel_1(B,A) )
     => k4_bvfunc_2(A,B) = k1_tarski(B) ) ),
    file(bvfunc_2,k4_bvfunc_2),
    [interesting(0.9),axiom,file(bvfunc_2,k4_bvfunc_2)]).

fof(dt_k2_bvfunc_2,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) )
     => m1_eqrel_1(k2_bvfunc_2(A,B),A) ) ),
    file(bvfunc_2,k2_bvfunc_2),
    [interesting(0.9),axiom,file(bvfunc_2,k2_bvfunc_2)]).

fof(dt_k4_bvfunc_2,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_eqrel_1(B,A) )
     => m1_subset_1(k4_bvfunc_2(A,B),k1_zfmisc_1(k1_bvfunc_2(A))) ) ),
    file(bvfunc_2,k4_bvfunc_2),
    [interesting(0.9),axiom,file(bvfunc_2,k4_bvfunc_2)]).

fof(dt_k5_bvfunc_2,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & m1_eqrel_1(B,A)
        & m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A))) )
     => m1_eqrel_1(k5_bvfunc_2(A,B,C),A) ) ),
    file(bvfunc_2,k5_bvfunc_2),
    [interesting(0.9),axiom,file(bvfunc_2,k5_bvfunc_2)]).

fof(dt_c1_7__bvfunc11,assumption,(
    ~ v1_xboole_0(c1_7__bvfunc11) ),
    introduced(assumption,[file(bvfunc11,c1_7__bvfunc11)]),
    [interesting(0.8),axiom,file(bvfunc11,c1_7__bvfunc11)]).

fof(dt_c2_7__bvfunc11,assumption,(
    m1_subset_1(c2_7__bvfunc11,k1_zfmisc_1(k1_bvfunc_2(c1_7__bvfunc11))) ),
    introduced(assumption,[file(bvfunc11,c2_7__bvfunc11)]),
    [interesting(0.8),axiom,file(bvfunc11,c2_7__bvfunc11)]).

fof(dt_c3_7__bvfunc11,assumption,(
    m1_eqrel_1(c3_7__bvfunc11,c1_7__bvfunc11) ),
    introduced(assumption,[file(bvfunc11,c3_7__bvfunc11)]),
    [interesting(0.8),axiom,file(bvfunc11,c3_7__bvfunc11)]).

fof(dt_c4_7__bvfunc11,assumption,(
    m1_eqrel_1(c4_7__bvfunc11,c1_7__bvfunc11) ),
    introduced(assumption,[file(bvfunc11,c4_7__bvfunc11)]),
    [interesting(0.8),axiom,file(bvfunc11,c4_7__bvfunc11)]).

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_7_3__bvfunc11,assumption,(
    $true ),
    introduced(assumption,[file(bvfunc11,c1_7_3__bvfunc11)]),
    [interesting(0.65),axiom,file(bvfunc11,c1_7_3__bvfunc11)]).

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_7_3__bvfunc11,definition,
    ( ~ ( r2_hidden(c1_7_3__bvfunc11,c4_7__bvfunc11)
        & ~ r2_hidden(c1_7_3__bvfunc11,k2_bvfunc_2(c1_7__bvfunc11,k4_bvfunc_2(c1_7__bvfunc11,c4_7__bvfunc11))) )
   => ! [A] : 
        ~ ( r2_hidden(A,c4_7__bvfunc11)
          & ~ r2_hidden(A,k2_bvfunc_2(c1_7__bvfunc11,k4_bvfunc_2(c1_7__bvfunc11,c4_7__bvfunc11))) ) ),
    introduced(definition,[new_symbol(c1_7_3__bvfunc11),file(bvfunc11,c1_7_3__bvfunc11)]),
    [interesting(0.65),axiom,file(bvfunc11,c1_7_3__bvfunc11)]).

fof(e1_7_3__bvfunc11,assumption,(
    r2_hidden(c1_7_3__bvfunc11,c4_7__bvfunc11) ),
    introduced(assumption,[file(bvfunc11,e1_7_3__bvfunc11)]),
    [interesting(0.65),axiom,file(bvfunc11,e1_7_3__bvfunc11)]).

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

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

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

fof(dt_k3_cqc_lang,axiom,(
    $true ),
    file(cqc_lang,k3_cqc_lang),
    [interesting(0.9),axiom,file(cqc_lang,k3_cqc_lang)]).

fof(dt_k8_setfam_1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => m1_subset_1(k8_setfam_1(A,B),k1_zfmisc_1(A)) ) ),
    file(setfam_1,k8_setfam_1),
    [interesting(0.9),axiom,file(setfam_1,k8_setfam_1)]).

fof(fc1_funct_7,theorem,(
    ! [A,B] : 
      ( ~ v1_xboole_0(k3_cqc_lang(A,B))
      & v1_relat_1(k3_cqc_lang(A,B))
      & v1_funct_1(k3_cqc_lang(A,B)) ) ),
    file(funct_7,fc1_funct_7),
    [interesting(0.9),axiom,file(funct_7,fc1_funct_7)]).

fof(de_c3_7_3__bvfunc11,definition,(
    c3_7_3__bvfunc11 = k2_relat_1(k3_cqc_lang(c4_7__bvfunc11,c1_7_3__bvfunc11)) ),
    introduced(definition,[new_symbol(c3_7_3__bvfunc11),file(bvfunc11,c3_7_3__bvfunc11)]),
    [interesting(0.65),axiom,file(bvfunc11,c3_7_3__bvfunc11)]).

fof(dt_c1_7_3_2__bvfunc11,assumption,(
    $true ),
    introduced(assumption,[file(bvfunc11,c1_7_3_2__bvfunc11)]),
    [interesting(0.5),axiom,file(bvfunc11,c1_7_3_2__bvfunc11)]).

fof(dh_c1_7_3_2__bvfunc11,definition,
    ( ~ ( r2_hidden(c1_7_3_2__bvfunc11,k2_relat_1(k3_cqc_lang(c4_7__bvfunc11,c1_7_3__bvfunc11)))
        & ~ r2_hidden(c1_7_3_2__bvfunc11,k1_zfmisc_1(c1_7__bvfunc11)) )
   => ! [A] : 
        ~ ( r2_hidden(A,k2_relat_1(k3_cqc_lang(c4_7__bvfunc11,c1_7_3__bvfunc11)))
          & ~ r2_hidden(A,k1_zfmisc_1(c1_7__bvfunc11)) ) ),
    introduced(definition,[new_symbol(c1_7_3_2__bvfunc11),file(bvfunc11,c1_7_3_2__bvfunc11)]),
    [interesting(0.5),axiom,file(bvfunc11,c1_7_3_2__bvfunc11)]).

fof(e1_7_3_2__bvfunc11,assumption,(
    r2_hidden(c1_7_3_2__bvfunc11,k2_relat_1(k3_cqc_lang(c4_7__bvfunc11,c1_7_3__bvfunc11))) ),
    introduced(assumption,[file(bvfunc11,e1_7_3_2__bvfunc11)]),
    [interesting(0.5),axiom,file(bvfunc11,e1_7_3_2__bvfunc11)]).

fof(t5_cqc_lang,theorem,(
    ! [A,B] : 
      ( k1_relat_1(k3_cqc_lang(A,B)) = k1_tarski(A)
      & k2_relat_1(k3_cqc_lang(A,B)) = k1_tarski(B) ) ),
    file(cqc_lang,t5_cqc_lang),
    [interesting(0.9),axiom,file(cqc_lang,t5_cqc_lang)]).

fof(e2_7_3__bvfunc11,plain,
    ( k1_relat_1(k3_cqc_lang(c4_7__bvfunc11,c1_7_3__bvfunc11)) = k4_bvfunc_2(c1_7__bvfunc11,c4_7__bvfunc11)
    & k2_relat_1(k3_cqc_lang(c4_7__bvfunc11,c1_7_3__bvfunc11)) = k1_tarski(c1_7_3__bvfunc11) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__bvfunc11,dt_c1_7_3__bvfunc11,dt_c4_7__bvfunc11])],[cc1_funct_7,cc2_funct_7,rc1_margrel1,reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_m1_t_1topsp,dt_k1_partit1,dt_k1_xboole_0,dt_m1_t_1topsp,fc1_margrel1,fc3_funct_7,t1_subset,t4_subset,t5_subset,existence_m1_eqrel_1,existence_m1_subset_1,redefinition_k1_bvfunc_2,dt_k1_bvfunc_2,dt_k1_zfmisc_1,dt_m1_eqrel_1,dt_m1_subset_1,cc1_eqrel_1,cc2_eqrel_1,fc1_subset_1,rc1_subset_1,rc2_subset_1,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,redefinition_k4_bvfunc_2,dt_k1_relat_1,dt_k1_tarski,dt_k2_relat_1,dt_k3_cqc_lang,dt_k4_bvfunc_2,dt_c1_7__bvfunc11,dt_c1_7_3__bvfunc11,dt_c4_7__bvfunc11,fc1_funct_7,fc2_subset_1,t5_cqc_lang]),
    [interesting(0.65),file(bvfunc11,e2_7_3__bvfunc11),[file(bvfunc11,e2_7_3__bvfunc11)]]).

fof(d1_tarski,definition,(
    ! [A,B] : 
      ( B = k1_tarski(A)
    <=> ! [C] : 
          ( r2_hidden(C,B)
        <=> C = A ) ) ),
    file(tarski,d1_tarski),
    [interesting(0.9),axiom,file(tarski,d1_tarski)]).

fof(e2_7_3_2__bvfunc11,plain,(
    c1_7_3_2__bvfunc11 = c1_7_3__bvfunc11 ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7_3_2__bvfunc11,e1_7_3_2__bvfunc11,dt_c1_7__bvfunc11,dt_c1_7_3__bvfunc11,dt_c4_7__bvfunc11])],[cc1_funct_7,cc2_funct_7,rc1_margrel1,reflexivity_r1_tarski,existence_m1_t_1topsp,dt_k1_partit1,dt_k1_xboole_0,dt_m1_t_1topsp,fc1_margrel1,fc3_funct_7,existence_m1_eqrel_1,existence_m1_subset_1,redefinition_k1_bvfunc_2,dt_k1_bvfunc_2,dt_k1_zfmisc_1,dt_m1_eqrel_1,dt_m1_subset_1,cc1_eqrel_1,cc2_eqrel_1,fc1_subset_1,rc1_subset_1,rc2_subset_1,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,redefinition_k4_bvfunc_2,dt_k1_relat_1,dt_k1_tarski,dt_k2_relat_1,dt_k3_cqc_lang,dt_k4_bvfunc_2,dt_c1_7__bvfunc11,dt_c1_7_3__bvfunc11,dt_c1_7_3_2__bvfunc11,dt_c4_7__bvfunc11,fc1_funct_7,fc2_subset_1,t1_subset,t7_boole,e1_7_3_2__bvfunc11,e2_7_3__bvfunc11,d1_tarski]),
    [interesting(0.5),file(bvfunc11,e2_7_3_2__bvfunc11),[file(bvfunc11,e2_7_3_2__bvfunc11)]]).

fof(e3_7_3_2__bvfunc11,plain,(
    r2_hidden(c1_7_3_2__bvfunc11,k1_zfmisc_1(c1_7__bvfunc11)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7_3_2__bvfunc11,e1_7_3_2__bvfunc11,dt_c1_7__bvfunc11,dt_c1_7_3__bvfunc11,dt_c4_7__bvfunc11,e1_7_3__bvfunc11])],[cc1_funct_7,cc2_funct_7,rc1_margrel1,reflexivity_r1_tarski,dt_k1_xboole_0,fc1_margrel1,fc3_funct_7,existence_m1_eqrel_1,existence_m1_subset_1,dt_m1_eqrel_1,dt_m1_subset_1,cc1_eqrel_1,cc2_eqrel_1,rc1_subset_1,rc2_subset_1,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_zfmisc_1,dt_c1_7__bvfunc11,dt_c1_7_3__bvfunc11,dt_c1_7_3_2__bvfunc11,dt_c4_7__bvfunc11,fc1_subset_1,t1_subset,t7_boole,e2_7_3_2__bvfunc11,e1_7_3__bvfunc11]),
    [interesting(0.5),file(bvfunc11,e3_7_3_2__bvfunc11),[file(bvfunc11,e3_7_3_2__bvfunc11)]]).

fof(i3_7_3_2__bvfunc11,theorem,(
    $true ),
    introduced(tautology,[file(bvfunc11,i3_7_3_2__bvfunc11)]),
    [interesting(0.5),trivial,file(bvfunc11,i3_7_3_2__bvfunc11)]).

fof(i2_7_3_2__bvfunc11,plain,(
    r2_hidden(c1_7_3_2__bvfunc11,k1_zfmisc_1(c1_7__bvfunc11)) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_7_3_2__bvfunc11,e1_7_3_2__bvfunc11,dt_c1_7__bvfunc11,dt_c1_7_3__bvfunc11,dt_c4_7__bvfunc11,e1_7_3__bvfunc11])],[e3_7_3_2__bvfunc11,i3_7_3_2__bvfunc11]),
    [interesting(0.5),file(bvfunc11,i2_7_3_2__bvfunc11),[file(bvfunc11,i2_7_3_2__bvfunc11)]]).

fof(i1_7_3_2__bvfunc11,plain,(
    ~ ( r2_hidden(c1_7_3_2__bvfunc11,k2_relat_1(k3_cqc_lang(c4_7__bvfunc11,c1_7_3__bvfunc11)))
      & ~ r2_hidden(c1_7_3_2__bvfunc11,k1_zfmisc_1(c1_7__bvfunc11)) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_7_3_2__bvfunc11,dt_c1_7__bvfunc11,dt_c1_7_3__bvfunc11,dt_c4_7__bvfunc11,e1_7_3__bvfunc11]),discharge_asm(discharge,[e1_7_3_2__bvfunc11])],[e1_7_3_2__bvfunc11,i2_7_3_2__bvfunc11]),
    [interesting(0.5),file(bvfunc11,i1_7_3_2__bvfunc11),[file(bvfunc11,i1_7_3_2__bvfunc11)]]).

fof(i1_7_3_2_tmp__bvfunc11,plain,(
    ~ ( r2_hidden(c1_7_3_2__bvfunc11,k2_relat_1(k3_cqc_lang(c4_7__bvfunc11,c1_7_3__bvfunc11)))
      & ~ r2_hidden(c1_7_3_2__bvfunc11,k1_zfmisc_1(c1_7__bvfunc11)) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_7__bvfunc11,dt_c1_7_3__bvfunc11,dt_c4_7__bvfunc11,e1_7_3__bvfunc11]),discharge_asm(discharge,[dt_c1_7_3_2__bvfunc11])],[dt_c1_7_3_2__bvfunc11,i1_7_3_2__bvfunc11]),
    [interesting(0.65),e4_7_3__bvfunc11]).

fof(e4_7_3__bvfunc11,plain,(
    r1_tarski(k2_relat_1(k3_cqc_lang(c4_7__bvfunc11,c1_7_3__bvfunc11)),k1_zfmisc_1(c1_7__bvfunc11)) ),
    inference(let,[status(thm),assumptions([dt_c1_7__bvfunc11,dt_c1_7_3__bvfunc11,dt_c4_7__bvfunc11,e1_7_3__bvfunc11])],[i1_7_3_2_tmp__bvfunc11,dt_m1_subset_1,rc1_subset_1,rc2_subset_1,dt_m1_eqrel_1,cc1_eqrel_1,cc2_eqrel_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_zfmisc_1,dt_k2_relat_1,dt_k3_cqc_lang,dt_c1_7__bvfunc11,dt_c1_7_3__bvfunc11,dt_c4_7__bvfunc11,fc1_funct_7,fc1_subset_1,d3_tarski,dh_c1_7_3_2__bvfunc11]),
    [interesting(0.65),file(bvfunc11,e4_7_3__bvfunc11),[file(bvfunc11,e4_7_3__bvfunc11)]]).

fof(e5_7_3__bvfunc11,plain,(
    m1_subset_1(k2_relat_1(k3_cqc_lang(c4_7__bvfunc11,c1_7_3__bvfunc11)),k1_zfmisc_1(k1_zfmisc_1(c1_7__bvfunc11))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__bvfunc11,dt_c1_7_3__bvfunc11,dt_c4_7__bvfunc11,e1_7_3__bvfunc11])],[cc1_funct_7,cc2_funct_7,rc1_margrel1,antisymmetry_r2_hidden,dt_k1_xboole_0,fc1_margrel1,fc3_funct_7,t1_subset,t4_subset,t5_subset,t8_boole,existence_m1_eqrel_1,dt_m1_eqrel_1,cc1_eqrel_1,cc2_eqrel_1,rc1_subset_1,rc2_subset_1,t2_subset,t6_boole,t7_boole,reflexivity_r1_tarski,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k2_relat_1,dt_k3_cqc_lang,dt_m1_subset_1,dt_c1_7__bvfunc11,dt_c1_7_3__bvfunc11,dt_c4_7__bvfunc11,fc1_funct_7,fc1_subset_1,t3_subset,e4_7_3__bvfunc11]),
    [interesting(0.65),file(bvfunc11,e5_7_3__bvfunc11),[file(bvfunc11,e5_7_3__bvfunc11)]]).

fof(dt_c3_7_3__bvfunc11,plain,(
    m1_subset_1(c3_7_3__bvfunc11,k1_zfmisc_1(k1_zfmisc_1(c1_7__bvfunc11))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__bvfunc11,dt_c1_7_3__bvfunc11,dt_c4_7__bvfunc11,e1_7_3__bvfunc11])],[cc1_funct_7,cc2_funct_7,rc1_margrel1,antisymmetry_r2_hidden,dt_k1_xboole_0,fc1_margrel1,fc3_funct_7,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,existence_m1_eqrel_1,dt_m1_eqrel_1,cc1_eqrel_1,cc2_eqrel_1,rc1_subset_1,rc2_subset_1,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k2_relat_1,dt_k3_cqc_lang,dt_m1_subset_1,dt_c1_7__bvfunc11,dt_c1_7_3__bvfunc11,dt_c4_7__bvfunc11,fc1_funct_7,fc1_subset_1,t3_subset,de_c3_7_3__bvfunc11,e5_7_3__bvfunc11]),
    [interesting(0.65),file(bvfunc11,c3_7_3__bvfunc11),[file(bvfunc11,c3_7_3__bvfunc11)]]).

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

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(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(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(e8_7_3__bvfunc11,plain,(
    c1_7_3__bvfunc11 != k1_xboole_0 ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__bvfunc11,dt_c1_7_3__bvfunc11,dt_c4_7__bvfunc11,e1_7_3__bvfunc11])],[cc1_funct_7,reflexivity_r1_tarski,dt_k3_tarski,dt_c1_7__bvfunc11,cc1_eqrel_1,cc2_funct_7,rc1_margrel1,rc1_subset_1,rc2_subset_1,t2_subset,t5_subset,t8_boole,symmetry_r1_xboole_0,antisymmetry_r2_hidden,existence_m1_eqrel_1,existence_m1_subset_1,redefinition_k5_setfam_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_setfam_1,dt_m1_eqrel_1,dt_m1_subset_1,dt_c1_7_3__bvfunc11,dt_c4_7__bvfunc11,cc2_eqrel_1,fc1_margrel1,fc1_subset_1,fc3_funct_7,t1_subset,t3_subset,t4_subset,t6_boole,t7_boole,e1_7_3__bvfunc11,d6_eqrel_1]),
    [interesting(0.65),file(bvfunc11,e8_7_3__bvfunc11),[file(bvfunc11,e8_7_3__bvfunc11)]]).

fof(dh_c1_7_3_1__bvfunc11,definition,
    ( ( r2_hidden(c1_7_3_1__bvfunc11,k4_bvfunc_2(c1_7__bvfunc11,c4_7__bvfunc11))
     => r2_hidden(k1_funct_1(k3_cqc_lang(c4_7__bvfunc11,c1_7_3__bvfunc11),c1_7_3_1__bvfunc11),c1_7_3_1__bvfunc11) )
   => ! [A] : 
        ( r2_hidden(A,k4_bvfunc_2(c1_7__bvfunc11,c4_7__bvfunc11))
       => r2_hidden(k1_funct_1(k3_cqc_lang(c4_7__bvfunc11,c1_7_3__bvfunc11),A),A) ) ),
    introduced(definition,[new_symbol(c1_7_3_1__bvfunc11),file(bvfunc11,c1_7_3_1__bvfunc11)]),
    [interesting(0.5),axiom,file(bvfunc11,c1_7_3_1__bvfunc11)]).

fof(e1_7_3_1__bvfunc11,assumption,(
    r2_hidden(c1_7_3_1__bvfunc11,k4_bvfunc_2(c1_7__bvfunc11,c4_7__bvfunc11)) ),
    introduced(assumption,[file(bvfunc11,e1_7_3_1__bvfunc11)]),
    [interesting(0.5),axiom,file(bvfunc11,e1_7_3_1__bvfunc11)]).

fof(dt_c1_7_3_1__bvfunc11,assumption,(
    $true ),
    introduced(assumption,[file(bvfunc11,c1_7_3_1__bvfunc11)]),
    [interesting(0.5),axiom,file(bvfunc11,c1_7_3_1__bvfunc11)]).

fof(e2_7_3_1__bvfunc11,plain,(
    c1_7_3_1__bvfunc11 = c4_7__bvfunc11 ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__bvfunc11,dt_c1_7_3_1__bvfunc11,dt_c4_7__bvfunc11,e1_7_3_1__bvfunc11])],[cc1_funct_7,cc2_funct_7,rc1_margrel1,reflexivity_r1_tarski,existence_m1_t_1topsp,dt_k1_partit1,dt_k1_xboole_0,dt_m1_t_1topsp,fc1_margrel1,fc3_funct_7,existence_m1_eqrel_1,existence_m1_subset_1,redefinition_k1_bvfunc_2,dt_k1_bvfunc_2,dt_k1_zfmisc_1,dt_m1_eqrel_1,dt_m1_subset_1,cc1_eqrel_1,cc2_eqrel_1,fc1_subset_1,rc1_subset_1,rc2_subset_1,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,redefinition_k4_bvfunc_2,dt_k1_tarski,dt_k4_bvfunc_2,dt_c1_7__bvfunc11,dt_c1_7_3_1__bvfunc11,dt_c4_7__bvfunc11,fc2_subset_1,t1_subset,t7_boole,e1_7_3_1__bvfunc11,d1_tarski]),
    [interesting(0.5),file(bvfunc11,e2_7_3_1__bvfunc11),[file(bvfunc11,e2_7_3_1__bvfunc11)]]).

fof(t6_cqc_lang,theorem,(
    ! [A,B] : k1_funct_1(k3_cqc_lang(A,B),A) = B ),
    file(cqc_lang,t6_cqc_lang),
    [interesting(0.9),axiom,file(cqc_lang,t6_cqc_lang)]).

fof(e3_7_3_1__bvfunc11,plain,(
    r2_hidden(k1_funct_1(k3_cqc_lang(c4_7__bvfunc11,c1_7_3__bvfunc11),c1_7_3_1__bvfunc11),c1_7_3_1__bvfunc11) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7_3__bvfunc11,dt_c1_7__bvfunc11,dt_c1_7_3_1__bvfunc11,dt_c4_7__bvfunc11,e1_7_3_1__bvfunc11,e1_7_3__bvfunc11])],[cc1_funct_7,reflexivity_r1_tarski,cc2_funct_7,rc1_margrel1,dt_k1_xboole_0,dt_k1_zfmisc_1,fc1_margrel1,fc1_subset_1,fc3_funct_7,rc1_subset_1,rc2_subset_1,t3_subset,t4_subset,t5_subset,existence_m1_eqrel_1,existence_m1_subset_1,dt_m1_eqrel_1,dt_m1_subset_1,dt_c1_7__bvfunc11,cc1_eqrel_1,cc2_eqrel_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k3_cqc_lang,dt_c1_7_3__bvfunc11,dt_c1_7_3_1__bvfunc11,dt_c4_7__bvfunc11,fc1_funct_7,t1_subset,t7_boole,e2_7_3_1__bvfunc11,e1_7_3__bvfunc11,t6_cqc_lang]),
    [interesting(0.5),file(bvfunc11,e3_7_3_1__bvfunc11),[file(bvfunc11,e3_7_3_1__bvfunc11)]]).

fof(i3_7_3_1__bvfunc11,theorem,(
    $true ),
    introduced(tautology,[file(bvfunc11,i3_7_3_1__bvfunc11)]),
    [interesting(0.5),trivial,file(bvfunc11,i3_7_3_1__bvfunc11)]).

fof(i2_7_3_1__bvfunc11,plain,(
    r2_hidden(k1_funct_1(k3_cqc_lang(c4_7__bvfunc11,c1_7_3__bvfunc11),c1_7_3_1__bvfunc11),c1_7_3_1__bvfunc11) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_7_3__bvfunc11,dt_c1_7__bvfunc11,dt_c1_7_3_1__bvfunc11,dt_c4_7__bvfunc11,e1_7_3_1__bvfunc11,e1_7_3__bvfunc11])],[e3_7_3_1__bvfunc11,i3_7_3_1__bvfunc11]),
    [interesting(0.5),file(bvfunc11,i2_7_3_1__bvfunc11),[file(bvfunc11,i2_7_3_1__bvfunc11)]]).

fof(i1_7_3_1__bvfunc11,plain,
    ( r2_hidden(c1_7_3_1__bvfunc11,k4_bvfunc_2(c1_7__bvfunc11,c4_7__bvfunc11))
   => r2_hidden(k1_funct_1(k3_cqc_lang(c4_7__bvfunc11,c1_7_3__bvfunc11),c1_7_3_1__bvfunc11),c1_7_3_1__bvfunc11) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_7_3__bvfunc11,dt_c1_7__bvfunc11,dt_c1_7_3_1__bvfunc11,dt_c4_7__bvfunc11,e1_7_3__bvfunc11]),discharge_asm(discharge,[e1_7_3_1__bvfunc11])],[e1_7_3_1__bvfunc11,i2_7_3_1__bvfunc11]),
    [interesting(0.5),file(bvfunc11,i1_7_3_1__bvfunc11),[file(bvfunc11,i1_7_3_1__bvfunc11)]]).

fof(i1_7_3_1_tmp__bvfunc11,plain,
    ( r2_hidden(c1_7_3_1__bvfunc11,k4_bvfunc_2(c1_7__bvfunc11,c4_7__bvfunc11))
   => r2_hidden(k1_funct_1(k3_cqc_lang(c4_7__bvfunc11,c1_7_3__bvfunc11),c1_7_3_1__bvfunc11),c1_7_3_1__bvfunc11) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_7_3__bvfunc11,dt_c1_7__bvfunc11,dt_c4_7__bvfunc11,e1_7_3__bvfunc11]),discharge_asm(discharge,[dt_c1_7_3_1__bvfunc11])],[dt_c1_7_3_1__bvfunc11,i1_7_3_1__bvfunc11]),
    [interesting(0.65),e3_7_3__bvfunc11]).

fof(e3_7_3__bvfunc11,plain,(
    ! [A] : 
      ( r2_hidden(A,k4_bvfunc_2(c1_7__bvfunc11,c4_7__bvfunc11))
     => r2_hidden(k1_funct_1(k3_cqc_lang(c4_7__bvfunc11,c1_7_3__bvfunc11),A),A) ) ),
    inference(let,[status(thm),assumptions([dt_c1_7_3__bvfunc11,dt_c1_7__bvfunc11,dt_c4_7__bvfunc11,e1_7_3__bvfunc11])],[i1_7_3_1_tmp__bvfunc11,dh_c1_7_3_1__bvfunc11]),
    [interesting(0.65),file(bvfunc11,e3_7_3__bvfunc11),[file(bvfunc11,e3_7_3__bvfunc11)]]).

fof(redefinition_k6_setfam_1,definition,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => k6_setfam_1(A,B) = k1_setfam_1(B) ) ),
    file(setfam_1,k6_setfam_1),
    [interesting(0.9),axiom,file(setfam_1,k6_setfam_1)]).

fof(dt_k1_setfam_1,axiom,(
    $true ),
    file(setfam_1,k1_setfam_1),
    [interesting(0.9),axiom,file(setfam_1,k1_setfam_1)]).

fof(dt_k6_setfam_1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => m1_subset_1(k6_setfam_1(A,B),k1_zfmisc_1(A)) ) ),
    file(setfam_1,k6_setfam_1),
    [interesting(0.9),axiom,file(setfam_1,k6_setfam_1)]).

fof(d10_setfam_1,definition,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ( ( B != k1_xboole_0
         => k8_setfam_1(A,B) = k6_setfam_1(A,B) )
        & ( B = k1_xboole_0
         => k8_setfam_1(A,B) = A ) ) ) ),
    file(setfam_1,d10_setfam_1),
    [interesting(0.9),axiom,file(setfam_1,d10_setfam_1)]).

fof(e6_7_3__bvfunc11,plain,(
    k6_setfam_1(c1_7__bvfunc11,c3_7_3__bvfunc11) = k8_setfam_1(c1_7__bvfunc11,c3_7_3__bvfunc11) ),
    inference(mizar_by,[status(thm),assumptions([e1_7_3__bvfunc11,dt_c1_7__bvfunc11,dt_c1_7_3__bvfunc11,dt_c4_7__bvfunc11])],[antisymmetry_r2_hidden,existence_m1_t_1topsp,dt_k1_partit1,dt_m1_t_1topsp,cc1_funct_7,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,existence_m1_eqrel_1,redefinition_k1_bvfunc_2,dt_k1_bvfunc_2,dt_k1_setfam_1,dt_m1_eqrel_1,cc1_eqrel_1,cc2_eqrel_1,cc2_funct_7,rc1_margrel1,rc1_subset_1,rc2_subset_1,t2_subset,t7_boole,t8_boole,existence_m1_subset_1,redefinition_k4_bvfunc_2,redefinition_k6_setfam_1,dt_k1_relat_1,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_relat_1,dt_k3_cqc_lang,dt_k4_bvfunc_2,dt_k6_setfam_1,dt_k8_setfam_1,dt_m1_subset_1,dt_c1_7__bvfunc11,dt_c1_7_3__bvfunc11,dt_c3_7_3__bvfunc11,dt_c4_7__bvfunc11,de_c3_7_3__bvfunc11,fc1_funct_7,fc1_margrel1,fc1_subset_1,fc2_subset_1,fc3_funct_7,t3_subset,t6_boole,e2_7_3__bvfunc11,d10_setfam_1]),
    [interesting(0.65),file(bvfunc11,e6_7_3__bvfunc11),[file(bvfunc11,e6_7_3__bvfunc11)]]).

fof(t11_setfam_1,theorem,(
    ! [A] : k1_setfam_1(k1_tarski(A)) = A ),
    file(setfam_1,t11_setfam_1),
    [interesting(0.9),axiom,file(setfam_1,t11_setfam_1)]).

fof(e7_7_3__bvfunc11,plain,(
    c1_7_3__bvfunc11 = k8_setfam_1(c1_7__bvfunc11,c3_7_3__bvfunc11) ),
    inference(mizar_by,[status(thm),assumptions([e1_7_3__bvfunc11,dt_c1_7__bvfunc11,dt_c1_7_3__bvfunc11,dt_c4_7__bvfunc11])],[cc1_funct_7,cc2_funct_7,rc1_margrel1,reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_m1_t_1topsp,dt_k1_partit1,dt_k1_xboole_0,dt_m1_t_1topsp,fc1_margrel1,fc3_funct_7,t1_subset,t4_subset,t5_subset,existence_m1_eqrel_1,existence_m1_subset_1,redefinition_k1_bvfunc_2,dt_k1_bvfunc_2,dt_k1_zfmisc_1,dt_m1_eqrel_1,dt_m1_subset_1,cc1_eqrel_1,cc2_eqrel_1,fc1_subset_1,rc1_subset_1,rc2_subset_1,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,redefinition_k4_bvfunc_2,redefinition_k6_setfam_1,dt_k1_relat_1,dt_k1_setfam_1,dt_k1_tarski,dt_k2_relat_1,dt_k3_cqc_lang,dt_k4_bvfunc_2,dt_k6_setfam_1,dt_k8_setfam_1,dt_c1_7__bvfunc11,dt_c1_7_3__bvfunc11,dt_c3_7_3__bvfunc11,dt_c4_7__bvfunc11,de_c3_7_3__bvfunc11,fc1_funct_7,fc2_subset_1,e6_7_3__bvfunc11,e2_7_3__bvfunc11,t11_setfam_1]),
    [interesting(0.65),file(bvfunc11,e7_7_3__bvfunc11),[file(bvfunc11,e7_7_3__bvfunc11)]]).

fof(d1_bvfunc_2,definition,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
         => ! [C] : 
              ( m1_eqrel_1(C,A)
             => ( C = k2_bvfunc_2(A,B)
              <=> ! [D] : 
                    ( r2_hidden(D,C)
                  <=> ? [E] : 
                        ( v1_relat_1(E)
                        & v1_funct_1(E)
                        & ? [F] : 
                            ( m1_subset_1(F,k1_zfmisc_1(k1_zfmisc_1(A)))
                            & k1_relat_1(E) = B
                            & k2_relat_1(E) = F
                            & ! [G] : 
                                ( r2_hidden(G,B)
                               => r2_hidden(k1_funct_1(E,G),G) )
                            & D = k8_setfam_1(A,F)
                            & D != k1_xboole_0 ) ) ) ) ) ) ) ),
    file(bvfunc_2,d1_bvfunc_2),
    [interesting(0.9),axiom,file(bvfunc_2,d1_bvfunc_2)]).

fof(e9_7_3__bvfunc11,plain,(
    r2_hidden(c1_7_3__bvfunc11,k2_bvfunc_2(c1_7__bvfunc11,k4_bvfunc_2(c1_7__bvfunc11,c4_7__bvfunc11))) ),
    inference(mizar_by,[status(thm),assumptions([e1_7_3__bvfunc11,dt_c1_7__bvfunc11,dt_c1_7_3__bvfunc11,dt_c4_7__bvfunc11])],[cc1_funct_7,reflexivity_r1_tarski,existence_m1_t_1topsp,dt_k1_partit1,dt_m1_t_1topsp,cc2_funct_7,rc1_margrel1,antisymmetry_r2_hidden,existence_m1_eqrel_1,existence_m1_subset_1,redefinition_k1_bvfunc_2,redefinition_k4_bvfunc_2,dt_k1_bvfunc_2,dt_k1_funct_1,dt_k1_relat_1,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_bvfunc_2,dt_k2_relat_1,dt_k3_cqc_lang,dt_k4_bvfunc_2,dt_k8_setfam_1,dt_m1_eqrel_1,dt_m1_subset_1,dt_c1_7__bvfunc11,dt_c1_7_3__bvfunc11,dt_c3_7_3__bvfunc11,dt_c4_7__bvfunc11,de_c3_7_3__bvfunc11,cc1_eqrel_1,cc2_eqrel_1,fc1_funct_7,fc1_margrel1,fc1_subset_1,fc2_subset_1,fc3_funct_7,rc1_subset_1,rc2_subset_1,t1_subset,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole,e8_7_3__bvfunc11,e2_7_3__bvfunc11,e3_7_3__bvfunc11,e7_7_3__bvfunc11,d1_bvfunc_2]),
    [interesting(0.65),file(bvfunc11,e9_7_3__bvfunc11),[file(bvfunc11,e9_7_3__bvfunc11)]]).

fof(i3_7_3__bvfunc11,theorem,(
    $true ),
    introduced(tautology,[file(bvfunc11,i3_7_3__bvfunc11)]),
    [interesting(0.65),trivial,file(bvfunc11,i3_7_3__bvfunc11)]).

fof(i2_7_3__bvfunc11,plain,(
    r2_hidden(c1_7_3__bvfunc11,k2_bvfunc_2(c1_7__bvfunc11,k4_bvfunc_2(c1_7__bvfunc11,c4_7__bvfunc11))) ),
    inference(conclusion,[status(thm),assumptions([e1_7_3__bvfunc11,dt_c1_7__bvfunc11,dt_c1_7_3__bvfunc11,dt_c4_7__bvfunc11])],[e9_7_3__bvfunc11,i3_7_3__bvfunc11]),
    [interesting(0.65),file(bvfunc11,i2_7_3__bvfunc11),[file(bvfunc11,i2_7_3__bvfunc11)]]).

fof(i1_7_3__bvfunc11,plain,(
    ~ ( r2_hidden(c1_7_3__bvfunc11,c4_7__bvfunc11)
      & ~ r2_hidden(c1_7_3__bvfunc11,k2_bvfunc_2(c1_7__bvfunc11,k4_bvfunc_2(c1_7__bvfunc11,c4_7__bvfunc11))) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_7__bvfunc11,dt_c1_7_3__bvfunc11,dt_c4_7__bvfunc11]),discharge_asm(discharge,[e1_7_3__bvfunc11])],[e1_7_3__bvfunc11,i2_7_3__bvfunc11]),
    [interesting(0.65),file(bvfunc11,i1_7_3__bvfunc11),[file(bvfunc11,i1_7_3__bvfunc11)]]).

fof(i1_7_3_tmp__bvfunc11,plain,(
    ~ ( r2_hidden(c1_7_3__bvfunc11,c4_7__bvfunc11)
      & ~ r2_hidden(c1_7_3__bvfunc11,k2_bvfunc_2(c1_7__bvfunc11,k4_bvfunc_2(c1_7__bvfunc11,c4_7__bvfunc11))) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_7__bvfunc11,dt_c4_7__bvfunc11]),discharge_asm(discharge,[dt_c1_7_3__bvfunc11])],[dt_c1_7_3__bvfunc11,i1_7_3__bvfunc11]),
    [interesting(0.8),e7_7__bvfunc11]).

fof(e7_7__bvfunc11,plain,(
    r1_tarski(c4_7__bvfunc11,k2_bvfunc_2(c1_7__bvfunc11,k4_bvfunc_2(c1_7__bvfunc11,c4_7__bvfunc11))) ),
    inference(let,[status(thm),assumptions([dt_c1_7__bvfunc11,dt_c4_7__bvfunc11])],[i1_7_3_tmp__bvfunc11,dt_k1_partit1,dt_m1_t_1topsp,redefinition_k1_bvfunc_2,dt_k1_bvfunc_2,dt_k1_tarski,dt_k1_zfmisc_1,dt_m1_eqrel_1,dt_m1_subset_1,cc1_eqrel_1,cc2_eqrel_1,fc1_subset_1,fc2_subset_1,rc1_subset_1,rc2_subset_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,redefinition_k4_bvfunc_2,dt_k2_bvfunc_2,dt_k4_bvfunc_2,dt_c1_7__bvfunc11,dt_c4_7__bvfunc11,d3_tarski,dh_c1_7_3__bvfunc11]),
    [interesting(0.8),file(bvfunc11,e7_7__bvfunc11),[file(bvfunc11,e7_7__bvfunc11)]]).

fof(commutativity_k2_xboole_0,theorem,(
    ! [A,B] : k2_xboole_0(A,B) = k2_xboole_0(B,A) ),
    file(xboole_0,k2_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k2_xboole_0)]).

fof(idempotence_k2_xboole_0,theorem,(
    ! [A,B] : k2_xboole_0(A,A) = A ),
    file(xboole_0,k2_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k2_xboole_0)]).

fof(dt_k2_xboole_0,axiom,(
    $true ),
    file(xboole_0,k2_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k2_xboole_0)]).

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

fof(t1_boole,theorem,(
    ! [A] : k2_xboole_0(A,k1_xboole_0) = A ),
    file(boole,t1_boole),
    [interesting(0.9),axiom,file(boole,t1_boole)]).

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(commutativity_k4_subset_1,theorem,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k4_subset_1(A,B,C) = k4_subset_1(A,C,B) ) ),
    file(subset_1,k4_subset_1),
    [interesting(0.9),axiom,file(subset_1,k4_subset_1)]).

fof(idempotence_k4_subset_1,theorem,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k4_subset_1(A,B,B) = B ) ),
    file(subset_1,k4_subset_1),
    [interesting(0.9),axiom,file(subset_1,k4_subset_1)]).

fof(redefinition_k4_subset_1,definition,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k4_subset_1(A,B,C) = k2_xboole_0(B,C) ) ),
    file(subset_1,k4_subset_1),
    [interesting(0.9),axiom,file(subset_1,k4_subset_1)]).

fof(redefinition_k6_subset_1,definition,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k6_subset_1(A,B,C) = k4_xboole_0(B,C) ) ),
    file(subset_1,k6_subset_1),
    [interesting(0.9),axiom,file(subset_1,k6_subset_1)]).

fof(dt_k4_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(k4_subset_1(A,B,C),k1_zfmisc_1(A)) ) ),
    file(subset_1,k4_subset_1),
    [interesting(0.9),axiom,file(subset_1,k4_subset_1)]).

fof(dt_k6_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(k6_subset_1(A,B,C),k1_zfmisc_1(A)) ) ),
    file(subset_1,k6_subset_1),
    [interesting(0.9),axiom,file(subset_1,k6_subset_1)]).

fof(e3_7__bvfunc11,plain,(
    r2_hidden(c3_7__bvfunc11,k4_bvfunc_2(c1_7__bvfunc11,c3_7__bvfunc11)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__bvfunc11,dt_c3_7__bvfunc11])],[cc1_funct_7,cc2_funct_7,rc1_margrel1,reflexivity_r1_tarski,existence_m1_t_1topsp,dt_k1_partit1,dt_k1_xboole_0,dt_m1_t_1topsp,fc1_margrel1,fc3_funct_7,existence_m1_eqrel_1,existence_m1_subset_1,redefinition_k1_bvfunc_2,dt_k1_bvfunc_2,dt_k1_zfmisc_1,dt_m1_eqrel_1,dt_m1_subset_1,cc1_eqrel_1,cc2_eqrel_1,fc1_subset_1,rc1_subset_1,rc2_subset_1,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,redefinition_k4_bvfunc_2,dt_k1_tarski,dt_k4_bvfunc_2,dt_c1_7__bvfunc11,dt_c3_7__bvfunc11,fc2_subset_1,t1_subset,t7_boole,d1_tarski]),
    [interesting(0.8),file(bvfunc11,e3_7__bvfunc11),[file(bvfunc11,e3_7__bvfunc11)]]).

fof(t68_zfmisc_1,theorem,(
    ! [A,B] : 
      ( k4_xboole_0(k1_tarski(A),B) = k1_xboole_0
    <=> r2_hidden(A,B) ) ),
    file(zfmisc_1,t68_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,t68_zfmisc_1)]).

fof(e4_7__bvfunc11,plain,(
    k6_subset_1(k1_bvfunc_2(c1_7__bvfunc11),k4_bvfunc_2(c1_7__bvfunc11,c3_7__bvfunc11),k4_bvfunc_2(c1_7__bvfunc11,c3_7__bvfunc11)) = k1_xboole_0 ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__bvfunc11,dt_c3_7__bvfunc11])],[reflexivity_r1_tarski,cc1_funct_7,existence_m1_eqrel_1,existence_m1_subset_1,existence_m1_t_1topsp,dt_k1_partit1,dt_k1_zfmisc_1,dt_m1_eqrel_1,dt_m1_subset_1,dt_m1_t_1topsp,cc1_eqrel_1,cc2_eqrel_1,cc2_funct_7,fc1_subset_1,rc1_margrel1,rc1_subset_1,rc2_subset_1,t2_subset,t3_subset,t4_subset,t5_subset,t8_boole,antisymmetry_r2_hidden,redefinition_k1_bvfunc_2,redefinition_k4_bvfunc_2,redefinition_k6_subset_1,dt_k1_bvfunc_2,dt_k1_tarski,dt_k1_xboole_0,dt_k4_bvfunc_2,dt_k4_xboole_0,dt_k6_subset_1,dt_c1_7__bvfunc11,dt_c3_7__bvfunc11,fc1_margrel1,fc2_subset_1,fc3_funct_7,t1_subset,t3_boole,t4_boole,t6_boole,t7_boole,e3_7__bvfunc11,t68_zfmisc_1]),
    [interesting(0.8),file(bvfunc11,e4_7__bvfunc11),[file(bvfunc11,e4_7__bvfunc11)]]).

fof(commutativity_k2_tarski,theorem,(
    ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ),
    file(tarski,k2_tarski),
    [interesting(0.9),axiom,file(tarski,k2_tarski)]).

fof(dt_k2_tarski,axiom,(
    $true ),
    file(tarski,k2_tarski),
    [interesting(0.9),axiom,file(tarski,k2_tarski)]).

fof(fc3_subset_1,theorem,(
    ! [A,B] : ~ v1_xboole_0(k2_tarski(A,B)) ),
    file(subset_1,fc3_subset_1),
    [interesting(0.9),axiom,file(subset_1,fc3_subset_1)]).

fof(t41_enumset1,theorem,(
    ! [A,B] : k2_tarski(A,B) = k2_xboole_0(k1_tarski(A),k1_tarski(B)) ),
    file(enumset1,t41_enumset1),
    [interesting(0.9),axiom,file(enumset1,t41_enumset1)]).

fof(e1_7_1__bvfunc11,plain,(
    k6_subset_1(k1_bvfunc_2(c1_7__bvfunc11),c2_7__bvfunc11,k4_bvfunc_2(c1_7__bvfunc11,c3_7__bvfunc11)) = k6_subset_1(k1_bvfunc_2(c1_7__bvfunc11),k4_subset_1(k1_bvfunc_2(c1_7__bvfunc11),k4_bvfunc_2(c1_7__bvfunc11,c3_7__bvfunc11),k4_bvfunc_2(c1_7__bvfunc11,c4_7__bvfunc11)),k4_bvfunc_2(c1_7__bvfunc11,c3_7__bvfunc11)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__bvfunc11,dt_c2_7__bvfunc11,dt_c3_7__bvfunc11,dt_c4_7__bvfunc11,e1_7__bvfunc11])],[cc1_funct_7,cc2_funct_7,rc1_margrel1,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,fc1_margrel1,fc3_funct_7,t1_boole,t1_subset,t3_boole,t4_boole,t4_subset,t5_subset,existence_m1_eqrel_1,existence_m1_subset_1,existence_m1_t_1topsp,dt_k1_partit1,dt_k1_zfmisc_1,dt_k4_xboole_0,dt_m1_eqrel_1,dt_m1_subset_1,dt_m1_t_1topsp,cc1_eqrel_1,cc2_eqrel_1,fc1_subset_1,rc1_subset_1,rc2_subset_1,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,commutativity_k2_tarski,commutativity_k2_xboole_0,idempotence_k2_xboole_0,commutativity_k4_subset_1,idempotence_k4_subset_1,redefinition_k1_bvfunc_2,redefinition_k4_bvfunc_2,redefinition_k4_subset_1,redefinition_k6_subset_1,dt_k1_bvfunc_2,dt_k1_tarski,dt_k2_tarski,dt_k2_xboole_0,dt_k4_bvfunc_2,dt_k4_subset_1,dt_k6_subset_1,dt_c1_7__bvfunc11,dt_c2_7__bvfunc11,dt_c3_7__bvfunc11,dt_c4_7__bvfunc11,fc2_subset_1,fc3_subset_1,e1_7__bvfunc11,t41_enumset1]),
    [interesting(0.65),file(bvfunc11,e1_7_1__bvfunc11),[file(bvfunc11,e1_7_1__bvfunc11)]]).

fof(t42_xboole_1,theorem,(
    ! [A,B,C] : k4_xboole_0(k2_xboole_0(A,B),C) = k2_xboole_0(k4_xboole_0(A,C),k4_xboole_0(B,C)) ),
    file(xboole_1,t42_xboole_1),
    [interesting(0.9),axiom,file(xboole_1,t42_xboole_1)]).

fof(e2_7_1__bvfunc11,plain,(
    k6_subset_1(k1_bvfunc_2(c1_7__bvfunc11),k4_subset_1(k1_bvfunc_2(c1_7__bvfunc11),k4_bvfunc_2(c1_7__bvfunc11,c3_7__bvfunc11),k4_bvfunc_2(c1_7__bvfunc11,c4_7__bvfunc11)),k4_bvfunc_2(c1_7__bvfunc11,c3_7__bvfunc11)) = k4_subset_1(k1_bvfunc_2(c1_7__bvfunc11),k6_subset_1(k1_bvfunc_2(c1_7__bvfunc11),k4_bvfunc_2(c1_7__bvfunc11,c3_7__bvfunc11),k4_bvfunc_2(c1_7__bvfunc11,c3_7__bvfunc11)),k6_subset_1(k1_bvfunc_2(c1_7__bvfunc11),k4_bvfunc_2(c1_7__bvfunc11,c4_7__bvfunc11),k4_bvfunc_2(c1_7__bvfunc11,c3_7__bvfunc11))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__bvfunc11,dt_c3_7__bvfunc11,dt_c4_7__bvfunc11])],[cc1_funct_7,cc2_funct_7,rc1_margrel1,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,fc1_margrel1,fc3_funct_7,t1_boole,t1_subset,t3_boole,t4_boole,t4_subset,t5_subset,existence_m1_eqrel_1,existence_m1_subset_1,existence_m1_t_1topsp,dt_k1_partit1,dt_k1_tarski,dt_k1_zfmisc_1,dt_m1_eqrel_1,dt_m1_subset_1,dt_m1_t_1topsp,cc1_eqrel_1,cc2_eqrel_1,fc1_subset_1,fc2_subset_1,rc1_subset_1,rc2_subset_1,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,commutativity_k4_subset_1,idempotence_k4_subset_1,redefinition_k1_bvfunc_2,redefinition_k4_bvfunc_2,redefinition_k4_subset_1,redefinition_k6_subset_1,dt_k1_bvfunc_2,dt_k2_xboole_0,dt_k4_bvfunc_2,dt_k4_subset_1,dt_k4_xboole_0,dt_k6_subset_1,dt_c1_7__bvfunc11,dt_c3_7__bvfunc11,dt_c4_7__bvfunc11,t42_xboole_1]),
    [interesting(0.65),file(bvfunc11,e2_7_1__bvfunc11),[file(bvfunc11,e2_7_1__bvfunc11)]]).

fof(t20_zfmisc_1,theorem,(
    ! [A,B] : 
      ( k4_xboole_0(k1_tarski(A),k1_tarski(B)) = k1_tarski(A)
    <=> A != B ) ),
    file(zfmisc_1,t20_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,t20_zfmisc_1)]).

fof(e3_7_1__bvfunc11,plain,(
    k4_subset_1(k1_bvfunc_2(c1_7__bvfunc11),k6_subset_1(k1_bvfunc_2(c1_7__bvfunc11),k4_bvfunc_2(c1_7__bvfunc11,c3_7__bvfunc11),k4_bvfunc_2(c1_7__bvfunc11,c3_7__bvfunc11)),k6_subset_1(k1_bvfunc_2(c1_7__bvfunc11),k4_bvfunc_2(c1_7__bvfunc11,c4_7__bvfunc11),k4_bvfunc_2(c1_7__bvfunc11,c3_7__bvfunc11))) = k4_subset_1(k1_bvfunc_2(c1_7__bvfunc11),k6_subset_1(k1_bvfunc_2(c1_7__bvfunc11),k4_bvfunc_2(c1_7__bvfunc11,c3_7__bvfunc11),k4_bvfunc_2(c1_7__bvfunc11,c3_7__bvfunc11)),k4_bvfunc_2(c1_7__bvfunc11,c4_7__bvfunc11)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__bvfunc11,dt_c2_7__bvfunc11,dt_c3_7__bvfunc11,dt_c4_7__bvfunc11,e1_7__bvfunc11])],[cc1_funct_7,cc2_funct_7,rc1_margrel1,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,fc1_margrel1,fc3_funct_7,t1_boole,t1_subset,t3_boole,t4_boole,t4_subset,t5_subset,commutativity_k2_xboole_0,idempotence_k2_xboole_0,existence_m1_eqrel_1,existence_m1_subset_1,existence_m1_t_1topsp,dt_k1_partit1,dt_k1_zfmisc_1,dt_k2_xboole_0,dt_m1_eqrel_1,dt_m1_subset_1,dt_m1_t_1topsp,cc1_eqrel_1,cc2_eqrel_1,fc1_subset_1,rc1_subset_1,rc2_subset_1,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,commutativity_k2_tarski,commutativity_k4_subset_1,idempotence_k4_subset_1,redefinition_k1_bvfunc_2,redefinition_k4_bvfunc_2,redefinition_k4_subset_1,redefinition_k6_subset_1,dt_k1_bvfunc_2,dt_k1_tarski,dt_k2_tarski,dt_k4_bvfunc_2,dt_k4_subset_1,dt_k4_xboole_0,dt_k6_subset_1,dt_c1_7__bvfunc11,dt_c2_7__bvfunc11,dt_c3_7__bvfunc11,dt_c4_7__bvfunc11,fc2_subset_1,fc3_subset_1,e1_7__bvfunc11,t20_zfmisc_1]),
    [interesting(0.65),file(bvfunc11,e3_7_1__bvfunc11),[file(bvfunc11,e3_7_1__bvfunc11)]]).

fof(e2_7__bvfunc11,plain,(
    k6_subset_1(k1_bvfunc_2(c1_7__bvfunc11),c2_7__bvfunc11,k4_bvfunc_2(c1_7__bvfunc11,c3_7__bvfunc11)) = k4_subset_1(k1_bvfunc_2(c1_7__bvfunc11),k6_subset_1(k1_bvfunc_2(c1_7__bvfunc11),k4_bvfunc_2(c1_7__bvfunc11,c3_7__bvfunc11),k4_bvfunc_2(c1_7__bvfunc11,c3_7__bvfunc11)),k4_bvfunc_2(c1_7__bvfunc11,c4_7__bvfunc11)) ),
    inference(iterative_eq,[status(thm),assumptions([dt_c1_7__bvfunc11,dt_c2_7__bvfunc11,dt_c3_7__bvfunc11,dt_c4_7__bvfunc11,e1_7__bvfunc11])],[e1_7_1__bvfunc11,e2_7_1__bvfunc11,e3_7_1__bvfunc11]),
    [interesting(0.8),file(bvfunc11,e2_7__bvfunc11),[file(bvfunc11,e2_7__bvfunc11)]]).

fof(d7_bvfunc_2,definition,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_eqrel_1(B,A)
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
             => k5_bvfunc_2(A,B,C) = k2_bvfunc_2(A,k6_subset_1(k1_bvfunc_2(A),C,k4_bvfunc_2(A,B))) ) ) ) ),
    file(bvfunc_2,d7_bvfunc_2),
    [interesting(0.9),axiom,file(bvfunc_2,d7_bvfunc_2)]).

fof(e5_7__bvfunc11,plain,(
    k5_bvfunc_2(c1_7__bvfunc11,c3_7__bvfunc11,c2_7__bvfunc11) = k2_bvfunc_2(c1_7__bvfunc11,k4_bvfunc_2(c1_7__bvfunc11,c4_7__bvfunc11)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__bvfunc11,dt_c2_7__bvfunc11,dt_c3_7__bvfunc11,dt_c4_7__bvfunc11,e1_7__bvfunc11])],[cc1_funct_7,commutativity_k2_xboole_0,idempotence_k2_xboole_0,reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_m1_t_1topsp,dt_k1_partit1,dt_k1_tarski,dt_k2_xboole_0,dt_k4_xboole_0,dt_m1_t_1topsp,cc2_funct_7,fc2_subset_1,rc1_margrel1,t1_boole,t1_subset,t3_boole,t4_boole,t4_subset,t5_subset,commutativity_k4_subset_1,idempotence_k4_subset_1,existence_m1_eqrel_1,existence_m1_subset_1,redefinition_k1_bvfunc_2,redefinition_k4_bvfunc_2,redefinition_k4_subset_1,redefinition_k6_subset_1,dt_k1_bvfunc_2,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_bvfunc_2,dt_k4_bvfunc_2,dt_k4_subset_1,dt_k5_bvfunc_2,dt_k6_subset_1,dt_m1_eqrel_1,dt_m1_subset_1,dt_c1_7__bvfunc11,dt_c2_7__bvfunc11,dt_c3_7__bvfunc11,dt_c4_7__bvfunc11,cc1_eqrel_1,cc2_eqrel_1,fc1_margrel1,fc1_subset_1,fc3_funct_7,rc1_subset_1,rc2_subset_1,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,e4_7__bvfunc11,e2_7__bvfunc11,d7_bvfunc_2]),
    [interesting(0.8),file(bvfunc11,e5_7__bvfunc11),[file(bvfunc11,e5_7__bvfunc11)]]).

fof(dt_c1_7_2__bvfunc11,assumption,(
    $true ),
    introduced(assumption,[file(bvfunc11,c1_7_2__bvfunc11)]),
    [interesting(0.65),axiom,file(bvfunc11,c1_7_2__bvfunc11)]).

fof(dh_c1_7_2__bvfunc11,definition,
    ( ~ ( r2_hidden(c1_7_2__bvfunc11,k2_bvfunc_2(c1_7__bvfunc11,k4_bvfunc_2(c1_7__bvfunc11,c4_7__bvfunc11)))
        & ~ r2_hidden(c1_7_2__bvfunc11,c4_7__bvfunc11) )
   => ! [A] : 
        ~ ( r2_hidden(A,k2_bvfunc_2(c1_7__bvfunc11,k4_bvfunc_2(c1_7__bvfunc11,c4_7__bvfunc11)))
          & ~ r2_hidden(A,c4_7__bvfunc11) ) ),
    introduced(definition,[new_symbol(c1_7_2__bvfunc11),file(bvfunc11,c1_7_2__bvfunc11)]),
    [interesting(0.65),axiom,file(bvfunc11,c1_7_2__bvfunc11)]).

fof(e1_7_2__bvfunc11,assumption,(
    r2_hidden(c1_7_2__bvfunc11,k2_bvfunc_2(c1_7__bvfunc11,k4_bvfunc_2(c1_7__bvfunc11,c4_7__bvfunc11))) ),
    introduced(assumption,[file(bvfunc11,e1_7_2__bvfunc11)]),
    [interesting(0.65),axiom,file(bvfunc11,e1_7_2__bvfunc11)]).

fof(dh_c2_7_2__bvfunc11,definition,
    ( ? [A] : 
        ( v1_relat_1(A)
        & v1_funct_1(A)
        & ? [B] : 
            ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(c1_7__bvfunc11)))
            & k1_relat_1(A) = k4_bvfunc_2(c1_7__bvfunc11,c4_7__bvfunc11)
            & k2_relat_1(A) = B
            & ! [C] : 
                ( r2_hidden(C,k4_bvfunc_2(c1_7__bvfunc11,c4_7__bvfunc11))
               => r2_hidden(k1_funct_1(A,C),C) )
            & c1_7_2__bvfunc11 = k8_setfam_1(c1_7__bvfunc11,B)
            & c1_7_2__bvfunc11 != k1_xboole_0 ) )
   => ( v1_relat_1(c2_7_2__bvfunc11)
      & v1_funct_1(c2_7_2__bvfunc11)
      & ? [D] : 
          ( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(c1_7__bvfunc11)))
          & k1_relat_1(c2_7_2__bvfunc11) = k4_bvfunc_2(c1_7__bvfunc11,c4_7__bvfunc11)
          & k2_relat_1(c2_7_2__bvfunc11) = D
          & ! [E] : 
              ( r2_hidden(E,k4_bvfunc_2(c1_7__bvfunc11,c4_7__bvfunc11))
             => r2_hidden(k1_funct_1(c2_7_2__bvfunc11,E),E) )
          & c1_7_2__bvfunc11 = k8_setfam_1(c1_7__bvfunc11,D)
          & c1_7_2__bvfunc11 != k1_xboole_0 ) ) ),
    introduced(definition,[new_symbol(c2_7_2__bvfunc11),file(bvfunc11,c2_7_2__bvfunc11)]),
    [interesting(0.65),axiom,file(bvfunc11,c2_7_2__bvfunc11)]).

fof(e2_7_2__bvfunc11,plain,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(c1_7__bvfunc11)))
          & k1_relat_1(A) = k4_bvfunc_2(c1_7__bvfunc11,c4_7__bvfunc11)
          & k2_relat_1(A) = B
          & ! [C] : 
              ( r2_hidden(C,k4_bvfunc_2(c1_7__bvfunc11,c4_7__bvfunc11))
             => r2_hidden(k1_funct_1(A,C),C) )
          & c1_7_2__bvfunc11 = k8_setfam_1(c1_7__bvfunc11,B)
          & c1_7_2__bvfunc11 != k1_xboole_0 ) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__bvfunc11,dt_c1_7_2__bvfunc11,dt_c4_7__bvfunc11,e1_7_2__bvfunc11])],[cc1_funct_7,reflexivity_r1_tarski,existence_m1_t_1topsp,dt_k1_partit1,dt_k1_tarski,dt_m1_t_1topsp,cc2_funct_7,fc2_subset_1,rc1_margrel1,antisymmetry_r2_hidden,existence_m1_eqrel_1,existence_m1_subset_1,redefinition_k1_bvfunc_2,redefinition_k4_bvfunc_2,dt_k1_bvfunc_2,dt_k1_funct_1,dt_k1_relat_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_bvfunc_2,dt_k2_relat_1,dt_k4_bvfunc_2,dt_k8_setfam_1,dt_m1_eqrel_1,dt_m1_subset_1,dt_c1_7__bvfunc11,dt_c1_7_2__bvfunc11,dt_c4_7__bvfunc11,cc1_eqrel_1,cc2_eqrel_1,fc1_margrel1,fc1_subset_1,fc3_funct_7,rc1_subset_1,rc2_subset_1,t1_subset,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole,e1_7_2__bvfunc11,d1_bvfunc_2]),
    [interesting(0.65),file(bvfunc11,e2_7_2__bvfunc11),[file(bvfunc11,e2_7_2__bvfunc11)]]).

fof(dt_c2_7_2__bvfunc11,plain,
    ( v1_relat_1(c2_7_2__bvfunc11)
    & v1_funct_1(c2_7_2__bvfunc11) ),
    inference(consider,[status(thm),assumptions([dt_c1_7__bvfunc11,dt_c1_7_2__bvfunc11,dt_c4_7__bvfunc11,e1_7_2__bvfunc11])],[dh_c2_7_2__bvfunc11,e2_7_2__bvfunc11]),
    [interesting(0.65),file(bvfunc11,c2_7_2__bvfunc11),[file(bvfunc11,c2_7_2__bvfunc11)]]).

fof(dh_c3_7_2__bvfunc11,definition,
    ( ? [A] : 
        ( m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(c1_7__bvfunc11)))
        & k1_relat_1(c2_7_2__bvfunc11) = k4_bvfunc_2(c1_7__bvfunc11,c4_7__bvfunc11)
        & k2_relat_1(c2_7_2__bvfunc11) = A
        & ! [B] : 
            ( r2_hidden(B,k4_bvfunc_2(c1_7__bvfunc11,c4_7__bvfunc11))
           => r2_hidden(k1_funct_1(c2_7_2__bvfunc11,B),B) )
        & c1_7_2__bvfunc11 = k8_setfam_1(c1_7__bvfunc11,A)
        & c1_7_2__bvfunc11 != k1_xboole_0 )
   => ( m1_subset_1(c3_7_2__bvfunc11,k1_zfmisc_1(k1_zfmisc_1(c1_7__bvfunc11)))
      & k1_relat_1(c2_7_2__bvfunc11) = k4_bvfunc_2(c1_7__bvfunc11,c4_7__bvfunc11)
      & k2_relat_1(c2_7_2__bvfunc11) = c3_7_2__bvfunc11
      & ! [C] : 
          ( r2_hidden(C,k4_bvfunc_2(c1_7__bvfunc11,c4_7__bvfunc11))
         => r2_hidden(k1_funct_1(c2_7_2__bvfunc11,C),C) )
      & c1_7_2__bvfunc11 = k8_setfam_1(c1_7__bvfunc11,c3_7_2__bvfunc11)
      & c1_7_2__bvfunc11 != k1_xboole_0 ) ),
    introduced(definition,[new_symbol(c3_7_2__bvfunc11),file(bvfunc11,c3_7_2__bvfunc11)]),
    [interesting(0.65),axiom,file(bvfunc11,c3_7_2__bvfunc11)]).

fof(dt_c3_7_2__bvfunc11,plain,(
    m1_subset_1(c3_7_2__bvfunc11,k1_zfmisc_1(k1_zfmisc_1(c1_7__bvfunc11))) ),
    inference(consider,[status(thm),assumptions([dt_c1_7__bvfunc11,dt_c1_7_2__bvfunc11,dt_c4_7__bvfunc11,e1_7_2__bvfunc11])],[dh_c2_7_2__bvfunc11,dh_c3_7_2__bvfunc11,e2_7_2__bvfunc11]),
    [interesting(0.65),file(bvfunc11,c3_7_2__bvfunc11),[file(bvfunc11,c3_7_2__bvfunc11)]]).

fof(e6_7_2__bvfunc11,plain,(
    r2_hidden(c4_7__bvfunc11,k4_bvfunc_2(c1_7__bvfunc11,c4_7__bvfunc11)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__bvfunc11,dt_c4_7__bvfunc11])],[cc1_funct_7,cc2_funct_7,rc1_margrel1,reflexivity_r1_tarski,existence_m1_t_1topsp,dt_k1_partit1,dt_k1_xboole_0,dt_m1_t_1topsp,fc1_margrel1,fc3_funct_7,existence_m1_eqrel_1,existence_m1_subset_1,redefinition_k1_bvfunc_2,dt_k1_bvfunc_2,dt_k1_zfmisc_1,dt_m1_eqrel_1,dt_m1_subset_1,cc1_eqrel_1,cc2_eqrel_1,fc1_subset_1,rc1_subset_1,rc2_subset_1,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,redefinition_k4_bvfunc_2,dt_k1_tarski,dt_k4_bvfunc_2,dt_c1_7__bvfunc11,dt_c4_7__bvfunc11,fc2_subset_1,t1_subset,t7_boole,d1_tarski]),
    [interesting(0.65),file(bvfunc11,e6_7_2__bvfunc11),[file(bvfunc11,e6_7_2__bvfunc11)]]).

fof(e3_7_2__bvfunc11,plain,
    ( k1_relat_1(c2_7_2__bvfunc11) = k4_bvfunc_2(c1_7__bvfunc11,c4_7__bvfunc11)
    & k2_relat_1(c2_7_2__bvfunc11) = c3_7_2__bvfunc11
    & ! [A] : 
        ( r2_hidden(A,k4_bvfunc_2(c1_7__bvfunc11,c4_7__bvfunc11))
       => r2_hidden(k1_funct_1(c2_7_2__bvfunc11,A),A) )
    & c1_7_2__bvfunc11 = k8_setfam_1(c1_7__bvfunc11,c3_7_2__bvfunc11)
    & c1_7_2__bvfunc11 != k1_xboole_0 ),
    inference(consider,[status(thm),assumptions([dt_c1_7__bvfunc11,dt_c1_7_2__bvfunc11,dt_c4_7__bvfunc11,e1_7_2__bvfunc11])],[dh_c2_7_2__bvfunc11,dh_c3_7_2__bvfunc11,e2_7_2__bvfunc11]),
    [interesting(0.65),file(bvfunc11,e3_7_2__bvfunc11),[file(bvfunc11,e3_7_2__bvfunc11)]]).

fof(e7_7_2__bvfunc11,plain,(
    r2_hidden(k1_funct_1(c2_7_2__bvfunc11,c4_7__bvfunc11),c4_7__bvfunc11) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__bvfunc11,dt_c1_7_2__bvfunc11,dt_c4_7__bvfunc11,e1_7_2__bvfunc11])],[reflexivity_r1_tarski,existence_m1_t_1topsp,dt_k1_partit1,dt_m1_t_1topsp,cc1_funct_7,existence_m1_eqrel_1,existence_m1_subset_1,redefinition_k1_bvfunc_2,dt_k1_bvfunc_2,dt_k1_tarski,dt_k1_zfmisc_1,dt_m1_eqrel_1,dt_m1_subset_1,cc1_eqrel_1,cc2_eqrel_1,cc2_funct_7,fc1_subset_1,fc2_subset_1,rc1_margrel1,rc1_subset_1,rc2_subset_1,t2_subset,t3_subset,t4_subset,t5_subset,t8_boole,antisymmetry_r2_hidden,redefinition_k4_bvfunc_2,dt_k1_funct_1,dt_k1_relat_1,dt_k1_xboole_0,dt_k2_relat_1,dt_k4_bvfunc_2,dt_k8_setfam_1,dt_c1_7__bvfunc11,dt_c1_7_2__bvfunc11,dt_c2_7_2__bvfunc11,dt_c3_7_2__bvfunc11,dt_c4_7__bvfunc11,fc1_margrel1,fc3_funct_7,t1_subset,t6_boole,t7_boole,e6_7_2__bvfunc11,e3_7_2__bvfunc11]),
    [interesting(0.65),file(bvfunc11,e7_7_2__bvfunc11),[file(bvfunc11,e7_7_2__bvfunc11)]]).

fof(t14_funct_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( k1_relat_1(B) = k1_tarski(A)
       => k2_relat_1(B) = k1_tarski(k1_funct_1(B,A)) ) ) ),
    file(funct_1,t14_funct_1),
    [interesting(0.9),axiom,file(funct_1,t14_funct_1)]).

fof(e4_7_2__bvfunc11,plain,(
    k2_relat_1(c2_7_2__bvfunc11) = k1_tarski(k1_funct_1(c2_7_2__bvfunc11,c4_7__bvfunc11)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__bvfunc11,dt_c1_7_2__bvfunc11,dt_c4_7__bvfunc11,e1_7_2__bvfunc11])],[reflexivity_r1_tarski,existence_m1_t_1topsp,dt_k1_partit1,dt_m1_t_1topsp,cc1_funct_7,existence_m1_eqrel_1,existence_m1_subset_1,redefinition_k1_bvfunc_2,dt_k1_bvfunc_2,dt_k1_zfmisc_1,dt_m1_eqrel_1,dt_m1_subset_1,cc1_eqrel_1,cc2_eqrel_1,cc2_funct_7,fc1_subset_1,rc1_margrel1,rc1_subset_1,rc2_subset_1,t2_subset,t3_subset,t4_subset,t5_subset,t8_boole,antisymmetry_r2_hidden,redefinition_k4_bvfunc_2,dt_k1_funct_1,dt_k1_relat_1,dt_k1_tarski,dt_k1_xboole_0,dt_k2_relat_1,dt_k4_bvfunc_2,dt_k8_setfam_1,dt_c1_7__bvfunc11,dt_c1_7_2__bvfunc11,dt_c2_7_2__bvfunc11,dt_c3_7_2__bvfunc11,dt_c4_7__bvfunc11,fc1_margrel1,fc2_subset_1,fc3_funct_7,t1_subset,t6_boole,t7_boole,e3_7_2__bvfunc11,t14_funct_1]),
    [interesting(0.65),file(bvfunc11,e4_7_2__bvfunc11),[file(bvfunc11,e4_7_2__bvfunc11)]]).

fof(e5_7_2__bvfunc11,plain,(
    c1_7_2__bvfunc11 = k1_setfam_1(k1_tarski(k1_funct_1(c2_7_2__bvfunc11,c4_7__bvfunc11))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__bvfunc11,dt_c1_7_2__bvfunc11,dt_c4_7__bvfunc11,e1_7_2__bvfunc11])],[existence_m1_t_1topsp,dt_k1_partit1,dt_m1_t_1topsp,cc1_funct_7,reflexivity_r1_tarski,existence_m1_eqrel_1,redefinition_k1_bvfunc_2,dt_k1_bvfunc_2,dt_m1_eqrel_1,cc1_eqrel_1,cc2_eqrel_1,cc2_funct_7,rc1_margrel1,rc1_subset_1,rc2_subset_1,t2_subset,t5_subset,t8_boole,antisymmetry_r2_hidden,existence_m1_subset_1,redefinition_k4_bvfunc_2,redefinition_k6_setfam_1,dt_k1_funct_1,dt_k1_relat_1,dt_k1_setfam_1,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_relat_1,dt_k4_bvfunc_2,dt_k6_setfam_1,dt_k8_setfam_1,dt_m1_subset_1,dt_c1_7__bvfunc11,dt_c1_7_2__bvfunc11,dt_c2_7_2__bvfunc11,dt_c3_7_2__bvfunc11,dt_c4_7__bvfunc11,fc1_margrel1,fc1_subset_1,fc2_subset_1,fc3_funct_7,t1_subset,t3_subset,t4_subset,t6_boole,t7_boole,e4_7_2__bvfunc11,e3_7_2__bvfunc11,d10_setfam_1]),
    [interesting(0.65),file(bvfunc11,e5_7_2__bvfunc11),[file(bvfunc11,e5_7_2__bvfunc11)]]).

fof(e8_7_2__bvfunc11,plain,(
    r2_hidden(c1_7_2__bvfunc11,c4_7__bvfunc11) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__bvfunc11,dt_c1_7_2__bvfunc11,dt_c4_7__bvfunc11,e1_7_2__bvfunc11])],[cc1_funct_7,reflexivity_r1_tarski,cc2_funct_7,rc1_margrel1,dt_k1_xboole_0,dt_k1_zfmisc_1,fc1_margrel1,fc1_subset_1,fc3_funct_7,rc1_subset_1,rc2_subset_1,t3_subset,t4_subset,t5_subset,existence_m1_eqrel_1,existence_m1_subset_1,dt_m1_eqrel_1,dt_m1_subset_1,dt_c1_7__bvfunc11,cc1_eqrel_1,cc2_eqrel_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_setfam_1,dt_k1_tarski,dt_c1_7_2__bvfunc11,dt_c2_7_2__bvfunc11,dt_c4_7__bvfunc11,fc2_subset_1,t1_subset,t7_boole,e7_7_2__bvfunc11,e5_7_2__bvfunc11,t11_setfam_1]),
    [interesting(0.65),file(bvfunc11,e8_7_2__bvfunc11),[file(bvfunc11,e8_7_2__bvfunc11)]]).

fof(i3_7_2__bvfunc11,theorem,(
    $true ),
    introduced(tautology,[file(bvfunc11,i3_7_2__bvfunc11)]),
    [interesting(0.65),trivial,file(bvfunc11,i3_7_2__bvfunc11)]).

fof(i2_7_2__bvfunc11,plain,(
    r2_hidden(c1_7_2__bvfunc11,c4_7__bvfunc11) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_7__bvfunc11,dt_c1_7_2__bvfunc11,dt_c4_7__bvfunc11,e1_7_2__bvfunc11])],[e8_7_2__bvfunc11,i3_7_2__bvfunc11]),
    [interesting(0.65),file(bvfunc11,i2_7_2__bvfunc11),[file(bvfunc11,i2_7_2__bvfunc11)]]).

fof(i1_7_2__bvfunc11,plain,(
    ~ ( r2_hidden(c1_7_2__bvfunc11,k2_bvfunc_2(c1_7__bvfunc11,k4_bvfunc_2(c1_7__bvfunc11,c4_7__bvfunc11)))
      & ~ r2_hidden(c1_7_2__bvfunc11,c4_7__bvfunc11) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_7__bvfunc11,dt_c1_7_2__bvfunc11,dt_c4_7__bvfunc11]),discharge_asm(discharge,[e1_7_2__bvfunc11])],[e1_7_2__bvfunc11,i2_7_2__bvfunc11]),
    [interesting(0.65),file(bvfunc11,i1_7_2__bvfunc11),[file(bvfunc11,i1_7_2__bvfunc11)]]).

fof(i1_7_2_tmp__bvfunc11,plain,(
    ~ ( r2_hidden(c1_7_2__bvfunc11,k2_bvfunc_2(c1_7__bvfunc11,k4_bvfunc_2(c1_7__bvfunc11,c4_7__bvfunc11)))
      & ~ r2_hidden(c1_7_2__bvfunc11,c4_7__bvfunc11) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_7__bvfunc11,dt_c4_7__bvfunc11]),discharge_asm(discharge,[dt_c1_7_2__bvfunc11])],[dt_c1_7_2__bvfunc11,i1_7_2__bvfunc11]),
    [interesting(0.8),e6_7__bvfunc11]).

fof(e6_7__bvfunc11,plain,(
    r1_tarski(k2_bvfunc_2(c1_7__bvfunc11,k4_bvfunc_2(c1_7__bvfunc11,c4_7__bvfunc11)),c4_7__bvfunc11) ),
    inference(let,[status(thm),assumptions([dt_c1_7__bvfunc11,dt_c4_7__bvfunc11])],[i1_7_2_tmp__bvfunc11,dt_k1_partit1,dt_m1_t_1topsp,redefinition_k1_bvfunc_2,dt_k1_bvfunc_2,dt_k1_tarski,dt_k1_zfmisc_1,dt_m1_eqrel_1,dt_m1_subset_1,cc1_eqrel_1,cc2_eqrel_1,fc1_subset_1,fc2_subset_1,rc1_subset_1,rc2_subset_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,redefinition_k4_bvfunc_2,dt_k2_bvfunc_2,dt_k4_bvfunc_2,dt_c1_7__bvfunc11,dt_c4_7__bvfunc11,d3_tarski,dh_c1_7_2__bvfunc11]),
    [interesting(0.8),file(bvfunc11,e6_7__bvfunc11),[file(bvfunc11,e6_7__bvfunc11)]]).

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(e8_7__bvfunc11,plain,(
    k5_bvfunc_2(c1_7__bvfunc11,c3_7__bvfunc11,c2_7__bvfunc11) = c4_7__bvfunc11 ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_7__bvfunc11,dt_c3_7__bvfunc11,e1_7__bvfunc11,dt_c1_7__bvfunc11,dt_c4_7__bvfunc11])],[cc1_funct_7,cc2_funct_7,rc1_margrel1,antisymmetry_r2_hidden,existence_m1_t_1topsp,dt_k1_partit1,dt_k1_xboole_0,dt_m1_t_1topsp,fc1_margrel1,fc3_funct_7,t1_subset,t4_subset,t5_subset,existence_m1_eqrel_1,existence_m1_subset_1,redefinition_k1_bvfunc_2,dt_k1_bvfunc_2,dt_k1_tarski,dt_k1_zfmisc_1,dt_m1_eqrel_1,dt_m1_subset_1,cc1_eqrel_1,cc2_eqrel_1,fc1_subset_1,fc2_subset_1,rc1_subset_1,rc2_subset_1,t2_subset,t6_boole,t7_boole,t8_boole,reflexivity_r1_tarski,redefinition_k4_bvfunc_2,dt_k2_bvfunc_2,dt_k4_bvfunc_2,dt_k5_bvfunc_2,dt_c1_7__bvfunc11,dt_c2_7__bvfunc11,dt_c3_7__bvfunc11,dt_c4_7__bvfunc11,t3_subset,e7_7__bvfunc11,e5_7__bvfunc11,e6_7__bvfunc11,d10_xboole_0]),
    [interesting(0.8),file(bvfunc11,e8_7__bvfunc11),[file(bvfunc11,e8_7__bvfunc11)]]).

fof(i5_7__bvfunc11,theorem,(
    $true ),
    introduced(tautology,[file(bvfunc11,i5_7__bvfunc11)]),
    [interesting(0.8),trivial,file(bvfunc11,i5_7__bvfunc11)]).

fof(i4_7__bvfunc11,plain,(
    k5_bvfunc_2(c1_7__bvfunc11,c3_7__bvfunc11,c2_7__bvfunc11) = c4_7__bvfunc11 ),
    inference(conclusion,[status(thm),assumptions([dt_c2_7__bvfunc11,dt_c3_7__bvfunc11,e1_7__bvfunc11,dt_c1_7__bvfunc11,dt_c4_7__bvfunc11])],[e8_7__bvfunc11,i5_7__bvfunc11]),
    [interesting(0.8),file(bvfunc11,i4_7__bvfunc11),[file(bvfunc11,i4_7__bvfunc11)]]).

fof(i3_7__bvfunc11,plain,
    ( c2_7__bvfunc11 = k2_tarski(c3_7__bvfunc11,c4_7__bvfunc11)
   => ( c3_7__bvfunc11 = c4_7__bvfunc11
      | k5_bvfunc_2(c1_7__bvfunc11,c3_7__bvfunc11,c2_7__bvfunc11) = c4_7__bvfunc11 ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c2_7__bvfunc11,dt_c3_7__bvfunc11,dt_c1_7__bvfunc11,dt_c4_7__bvfunc11]),discharge_asm(discharge,[e1_7__bvfunc11])],[e1_7__bvfunc11,i4_7__bvfunc11]),
    [interesting(0.8),file(bvfunc11,i3_7__bvfunc11),[file(bvfunc11,i3_7__bvfunc11)]]).

fof(i3_7_tmp__bvfunc11,plain,
    ( ( m1_eqrel_1(c3_7__bvfunc11,c1_7__bvfunc11)
      & m1_eqrel_1(c4_7__bvfunc11,c1_7__bvfunc11) )
   => ( c2_7__bvfunc11 = k2_tarski(c3_7__bvfunc11,c4_7__bvfunc11)
     => ( c3_7__bvfunc11 = c4_7__bvfunc11
        | k5_bvfunc_2(c1_7__bvfunc11,c3_7__bvfunc11,c2_7__bvfunc11) = c4_7__bvfunc11 ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c2_7__bvfunc11,dt_c1_7__bvfunc11]),discharge_asm(discharge,[dt_c3_7__bvfunc11,dt_c4_7__bvfunc11])],[dt_c3_7__bvfunc11,dt_c4_7__bvfunc11,i3_7__bvfunc11]),
    [interesting(0.8),i2_7__bvfunc11]).

fof(i2_7__bvfunc11,plain,(
    ! [A] : 
      ( m1_eqrel_1(A,c1_7__bvfunc11)
     => ! [B] : 
          ( m1_eqrel_1(B,c1_7__bvfunc11)
         => ( c2_7__bvfunc11 = k2_tarski(A,B)
           => ( A = B
              | k5_bvfunc_2(c1_7__bvfunc11,A,c2_7__bvfunc11) = B ) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c2_7__bvfunc11,dt_c1_7__bvfunc11])],[i3_7_tmp__bvfunc11,dh_c3_7__bvfunc11,dh_c4_7__bvfunc11]),
    [interesting(0.8),file(bvfunc11,i2_7__bvfunc11),[file(bvfunc11,i2_7__bvfunc11)]]).

fof(i2_7_tmp__bvfunc11,plain,
    ( m1_subset_1(c2_7__bvfunc11,k1_zfmisc_1(k1_bvfunc_2(c1_7__bvfunc11)))
   => ! [A] : 
        ( m1_eqrel_1(A,c1_7__bvfunc11)
       => ! [B] : 
            ( m1_eqrel_1(B,c1_7__bvfunc11)
           => ( c2_7__bvfunc11 = k2_tarski(A,B)
             => ( A = B
                | k5_bvfunc_2(c1_7__bvfunc11,A,c2_7__bvfunc11) = B ) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_7__bvfunc11]),discharge_asm(discharge,[dt_c2_7__bvfunc11])],[dt_c2_7__bvfunc11,i2_7__bvfunc11]),
    [interesting(0.8),i1_7__bvfunc11]).

fof(i1_7__bvfunc11,plain,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_bvfunc_2(c1_7__bvfunc11)))
     => ! [B] : 
          ( m1_eqrel_1(B,c1_7__bvfunc11)
         => ! [C] : 
              ( m1_eqrel_1(C,c1_7__bvfunc11)
             => ( A = k2_tarski(B,C)
               => ( B = C
                  | k5_bvfunc_2(c1_7__bvfunc11,B,A) = C ) ) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_7__bvfunc11])],[i2_7_tmp__bvfunc11,dh_c2_7__bvfunc11]),
    [interesting(0.8),file(bvfunc11,i1_7__bvfunc11),[file(bvfunc11,i1_7__bvfunc11)]]).

fof(i1_7_tmp__bvfunc11,plain,
    ( ~ v1_xboole_0(c1_7__bvfunc11)
   => ! [A] : 
        ( m1_subset_1(A,k1_zfmisc_1(k1_bvfunc_2(c1_7__bvfunc11)))
       => ! [B] : 
            ( m1_eqrel_1(B,c1_7__bvfunc11)
           => ! [C] : 
                ( m1_eqrel_1(C,c1_7__bvfunc11)
               => ( A = k2_tarski(B,C)
                 => ( B = C
                    | k5_bvfunc_2(c1_7__bvfunc11,B,A) = C ) ) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_7__bvfunc11])],[dt_c1_7__bvfunc11,i1_7__bvfunc11]),
    [interesting(1),t7_bvfunc11]).

fof(t7_bvfunc11,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
         => ! [C] : 
              ( m1_eqrel_1(C,A)
             => ! [D] : 
                  ( m1_eqrel_1(D,A)
                 => ( B = k2_tarski(C,D)
                   => ( C = D
                      | k5_bvfunc_2(A,C,B) = D ) ) ) ) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_7_tmp__bvfunc11,dh_c1_7__bvfunc11]),
    [interesting(1),file(bvfunc11,t7_bvfunc11),[file(bvfunc11,t7_bvfunc11)]]).