% Mizar ND problem: t5_bvfunc11,bvfunc11,71,50 
fof(dh_c1_5__bvfunc11,definition,
    ( ( ~ v1_xboole_0(c1_5__bvfunc11)
     => ! [A] : 
          ( m1_subset_1(A,k1_zfmisc_1(k1_bvfunc_2(c1_5__bvfunc11)))
         => ! [B] : 
              ( m1_eqrel_1(B,c1_5__bvfunc11)
             => ! [C] : 
                  ( m1_eqrel_1(C,c1_5__bvfunc11)
                 => ( ( v2_bvfunc_2(A,c1_5__bvfunc11)
                      & A = k2_tarski(B,C) )
                   => ( B = C
                      | ! [D,E] : 
                          ~ ( r2_hidden(D,B)
                            & r2_hidden(E,C)
                            & r1_xboole_0(D,E) ) ) ) ) ) ) )
   => ! [F] : 
        ( ~ v1_xboole_0(F)
       => ! [G] : 
            ( m1_subset_1(G,k1_zfmisc_1(k1_bvfunc_2(F)))
           => ! [H] : 
                ( m1_eqrel_1(H,F)
               => ! [I] : 
                    ( m1_eqrel_1(I,F)
                   => ( ( v2_bvfunc_2(G,F)
                        & G = k2_tarski(H,I) )
                     => ( H = I
                        | ! [J,K] : 
                            ~ ( r2_hidden(J,H)
                              & r2_hidden(K,I)
                              & r1_xboole_0(J,K) ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbol(c1_5__bvfunc11),file(bvfunc11,c1_5__bvfunc11)]),
    [interesting(0.8),axiom,file(bvfunc11,c1_5__bvfunc11)]).

fof(dh_c2_5__bvfunc11,definition,
    ( ( m1_subset_1(c2_5__bvfunc11,k1_zfmisc_1(k1_bvfunc_2(c1_5__bvfunc11)))
     => ! [A] : 
          ( m1_eqrel_1(A,c1_5__bvfunc11)
         => ! [B] : 
              ( m1_eqrel_1(B,c1_5__bvfunc11)
             => ( ( v2_bvfunc_2(c2_5__bvfunc11,c1_5__bvfunc11)
                  & c2_5__bvfunc11 = k2_tarski(A,B) )
               => ( A = B
                  | ! [C,D] : 
                      ~ ( r2_hidden(C,A)
                        & r2_hidden(D,B)
                        & r1_xboole_0(C,D) ) ) ) ) ) )
   => ! [E] : 
        ( m1_subset_1(E,k1_zfmisc_1(k1_bvfunc_2(c1_5__bvfunc11)))
       => ! [F] : 
            ( m1_eqrel_1(F,c1_5__bvfunc11)
           => ! [G] : 
                ( m1_eqrel_1(G,c1_5__bvfunc11)
               => ( ( v2_bvfunc_2(E,c1_5__bvfunc11)
                    & E = k2_tarski(F,G) )
                 => ( F = G
                    | ! [H,I] : 
                        ~ ( r2_hidden(H,F)
                          & r2_hidden(I,G)
                          & r1_xboole_0(H,I) ) ) ) ) ) ) ),
    introduced(definition,[new_symbol(c2_5__bvfunc11),file(bvfunc11,c2_5__bvfunc11)]),
    [interesting(0.8),axiom,file(bvfunc11,c2_5__bvfunc11)]).

fof(dh_c3_5__bvfunc11,definition,
    ( ( m1_eqrel_1(c3_5__bvfunc11,c1_5__bvfunc11)
     => ! [A] : 
          ( m1_eqrel_1(A,c1_5__bvfunc11)
         => ( ( v2_bvfunc_2(c2_5__bvfunc11,c1_5__bvfunc11)
              & c2_5__bvfunc11 = k2_tarski(c3_5__bvfunc11,A) )
           => ( c3_5__bvfunc11 = A
              | ! [B,C] : 
                  ~ ( r2_hidden(B,c3_5__bvfunc11)
                    & r2_hidden(C,A)
                    & r1_xboole_0(B,C) ) ) ) ) )
   => ! [D] : 
        ( m1_eqrel_1(D,c1_5__bvfunc11)
       => ! [E] : 
            ( m1_eqrel_1(E,c1_5__bvfunc11)
           => ( ( v2_bvfunc_2(c2_5__bvfunc11,c1_5__bvfunc11)
                & c2_5__bvfunc11 = k2_tarski(D,E) )
             => ( D = E
                | ! [F,G] : 
                    ~ ( r2_hidden(F,D)
                      & r2_hidden(G,E)
                      & r1_xboole_0(F,G) ) ) ) ) ) ),
    introduced(definition,[new_symbol(c3_5__bvfunc11),file(bvfunc11,c3_5__bvfunc11)]),
    [interesting(0.8),axiom,file(bvfunc11,c3_5__bvfunc11)]).

fof(dh_c4_5__bvfunc11,definition,
    ( ( m1_eqrel_1(c4_5__bvfunc11,c1_5__bvfunc11)
     => ( ( v2_bvfunc_2(c2_5__bvfunc11,c1_5__bvfunc11)
          & c2_5__bvfunc11 = k2_tarski(c3_5__bvfunc11,c4_5__bvfunc11) )
       => ( c3_5__bvfunc11 = c4_5__bvfunc11
          | ! [A,B] : 
              ~ ( r2_hidden(A,c3_5__bvfunc11)
                & r2_hidden(B,c4_5__bvfunc11)
                & r1_xboole_0(A,B) ) ) ) )
   => ! [C] : 
        ( m1_eqrel_1(C,c1_5__bvfunc11)
       => ( ( v2_bvfunc_2(c2_5__bvfunc11,c1_5__bvfunc11)
            & c2_5__bvfunc11 = k2_tarski(c3_5__bvfunc11,C) )
         => ( c3_5__bvfunc11 = C
            | ! [D,E] : 
                ~ ( r2_hidden(D,c3_5__bvfunc11)
                  & r2_hidden(E,C)
                  & r1_xboole_0(D,E) ) ) ) ) ),
    introduced(definition,[new_symbol(c4_5__bvfunc11),file(bvfunc11,c4_5__bvfunc11)]),
    [interesting(0.8),axiom,file(bvfunc11,c4_5__bvfunc11)]).

fof(e1_5__bvfunc11,assumption,(
    v2_bvfunc_2(c2_5__bvfunc11,c1_5__bvfunc11) ),
    introduced(assumption,[file(bvfunc11,e1_5__bvfunc11)]),
    [interesting(0.8),axiom,file(bvfunc11,e1_5__bvfunc11)]).

fof(e2_5__bvfunc11,assumption,
    ( c2_5__bvfunc11 = k2_tarski(c3_5__bvfunc11,c4_5__bvfunc11)
    & c3_5__bvfunc11 != c4_5__bvfunc11 ),
    introduced(assumption,[file(bvfunc11,e2_5__bvfunc11)]),
    [interesting(0.8),axiom,file(bvfunc11,e2_5__bvfunc11)]).

fof(dh_c5_5__bvfunc11,definition,
    ( ! [A] : 
        ~ ( r2_hidden(c5_5__bvfunc11,c3_5__bvfunc11)
          & r2_hidden(A,c4_5__bvfunc11)
          & r1_xboole_0(c5_5__bvfunc11,A) )
   => ! [B,C] : 
        ~ ( r2_hidden(B,c3_5__bvfunc11)
          & r2_hidden(C,c4_5__bvfunc11)
          & r1_xboole_0(B,C) ) ),
    introduced(definition,[new_symbol(c5_5__bvfunc11),file(bvfunc11,c5_5__bvfunc11)]),
    [interesting(0.8),axiom,file(bvfunc11,c5_5__bvfunc11)]).

fof(dh_c6_5__bvfunc11,definition,
    ( ~ ( r2_hidden(c5_5__bvfunc11,c3_5__bvfunc11)
        & r2_hidden(c6_5__bvfunc11,c4_5__bvfunc11)
        & r1_xboole_0(c5_5__bvfunc11,c6_5__bvfunc11) )
   => ! [A] : 
        ~ ( r2_hidden(c5_5__bvfunc11,c3_5__bvfunc11)
          & r2_hidden(A,c4_5__bvfunc11)
          & r1_xboole_0(c5_5__bvfunc11,A) ) ),
    introduced(definition,[new_symbol(c6_5__bvfunc11),file(bvfunc11,c6_5__bvfunc11)]),
    [interesting(0.8),axiom,file(bvfunc11,c6_5__bvfunc11)]).

fof(e3_5__bvfunc11,assumption,
    ( r2_hidden(c5_5__bvfunc11,c3_5__bvfunc11)
    & r2_hidden(c6_5__bvfunc11,c4_5__bvfunc11) ),
    introduced(assumption,[file(bvfunc11,e3_5__bvfunc11)]),
    [interesting(0.8),axiom,file(bvfunc11,e3_5__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(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(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(dt_k1_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k1_xboole_0)]).

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_c5_5__bvfunc11,assumption,(
    $true ),
    introduced(assumption,[file(bvfunc11,c5_5__bvfunc11)]),
    [interesting(0.8),axiom,file(bvfunc11,c5_5__bvfunc11)]).

fof(dt_c6_5__bvfunc11,assumption,(
    $true ),
    introduced(assumption,[file(bvfunc11,c6_5__bvfunc11)]),
    [interesting(0.8),axiom,file(bvfunc11,c6_5__bvfunc11)]).

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(d7_xboole_0,definition,(
    ! [A,B] : 
      ( r1_xboole_0(A,B)
    <=> k3_xboole_0(A,B) = k1_xboole_0 ) ),
    file(xboole_0,d7_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,d7_xboole_0)]).

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

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(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(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(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(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(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_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(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(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_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_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_k1_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k1_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,k1_zfmisc_1)]).

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

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

fof(dt_c1_5__bvfunc11,assumption,(
    ~ v1_xboole_0(c1_5__bvfunc11) ),
    introduced(assumption,[file(bvfunc11,c1_5__bvfunc11)]),
    [interesting(0.8),axiom,file(bvfunc11,c1_5__bvfunc11)]).

fof(dt_c3_5__bvfunc11,assumption,(
    m1_eqrel_1(c3_5__bvfunc11,c1_5__bvfunc11) ),
    introduced(assumption,[file(bvfunc11,c3_5__bvfunc11)]),
    [interesting(0.8),axiom,file(bvfunc11,c3_5__bvfunc11)]).

fof(dt_c4_5__bvfunc11,assumption,(
    m1_eqrel_1(c4_5__bvfunc11,c1_5__bvfunc11) ),
    introduced(assumption,[file(bvfunc11,c4_5__bvfunc11)]),
    [interesting(0.8),axiom,file(bvfunc11,c4_5__bvfunc11)]).

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(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(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(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(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(de_c8_5__bvfunc11,definition,(
    c8_5__bvfunc11 = k2_tarski(c5_5__bvfunc11,c6_5__bvfunc11) ),
    introduced(definition,[new_symbol(c8_5__bvfunc11),file(bvfunc11,c8_5__bvfunc11)]),
    [interesting(0.8),axiom,file(bvfunc11,c8_5__bvfunc11)]).

fof(dt_c1_5_1__bvfunc11,assumption,(
    $true ),
    introduced(assumption,[file(bvfunc11,c1_5_1__bvfunc11)]),
    [interesting(0.65),axiom,file(bvfunc11,c1_5_1__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_5_1__bvfunc11,definition,
    ( ~ ( r2_hidden(c1_5_1__bvfunc11,k2_tarski(c5_5__bvfunc11,c6_5__bvfunc11))
        & ~ r2_hidden(c1_5_1__bvfunc11,k1_zfmisc_1(c1_5__bvfunc11)) )
   => ! [A] : 
        ~ ( r2_hidden(A,k2_tarski(c5_5__bvfunc11,c6_5__bvfunc11))
          & ~ r2_hidden(A,k1_zfmisc_1(c1_5__bvfunc11)) ) ),
    introduced(definition,[new_symbol(c1_5_1__bvfunc11),file(bvfunc11,c1_5_1__bvfunc11)]),
    [interesting(0.65),axiom,file(bvfunc11,c1_5_1__bvfunc11)]).

fof(e1_5_1__bvfunc11,assumption,(
    r2_hidden(c1_5_1__bvfunc11,k2_tarski(c5_5__bvfunc11,c6_5__bvfunc11)) ),
    introduced(assumption,[file(bvfunc11,e1_5_1__bvfunc11)]),
    [interesting(0.65),axiom,file(bvfunc11,e1_5_1__bvfunc11)]).

fof(d2_tarski,definition,(
    ! [A,B,C] : 
      ( C = k2_tarski(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( D = A
            | D = B ) ) ) ),
    file(tarski,d2_tarski),
    [interesting(0.9),axiom,file(tarski,d2_tarski)]).

fof(e2_5_1__bvfunc11,plain,
    ( c1_5_1__bvfunc11 = c5_5__bvfunc11
    | c1_5_1__bvfunc11 = c6_5__bvfunc11 ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5_1__bvfunc11,dt_c5_5__bvfunc11,dt_c6_5__bvfunc11,e1_5_1__bvfunc11])],[cc1_funct_7,cc2_funct_7,rc1_margrel1,dt_k1_xboole_0,fc1_margrel1,fc3_funct_7,existence_m1_subset_1,dt_m1_subset_1,t2_subset,t6_boole,t8_boole,commutativity_k2_tarski,antisymmetry_r2_hidden,dt_k2_tarski,dt_c1_5_1__bvfunc11,dt_c5_5__bvfunc11,dt_c6_5__bvfunc11,fc3_subset_1,t1_subset,t7_boole,e1_5_1__bvfunc11,d2_tarski]),
    [interesting(0.65),file(bvfunc11,e2_5_1__bvfunc11),[file(bvfunc11,e2_5_1__bvfunc11)]]).

fof(e3_5_1__bvfunc11,plain,(
    r2_hidden(c1_5_1__bvfunc11,k1_zfmisc_1(c1_5__bvfunc11)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5__bvfunc11,dt_c3_5__bvfunc11,dt_c4_5__bvfunc11,dt_c1_5_1__bvfunc11,dt_c5_5__bvfunc11,dt_c6_5__bvfunc11,e1_5_1__bvfunc11,e3_5__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_5__bvfunc11,dt_c1_5_1__bvfunc11,dt_c3_5__bvfunc11,dt_c4_5__bvfunc11,dt_c5_5__bvfunc11,dt_c6_5__bvfunc11,fc1_subset_1,t1_subset,t7_boole,e2_5_1__bvfunc11,e3_5__bvfunc11]),
    [interesting(0.65),file(bvfunc11,e3_5_1__bvfunc11),[file(bvfunc11,e3_5_1__bvfunc11)]]).

fof(i3_5_1__bvfunc11,theorem,(
    $true ),
    introduced(tautology,[file(bvfunc11,i3_5_1__bvfunc11)]),
    [interesting(0.65),trivial,file(bvfunc11,i3_5_1__bvfunc11)]).

fof(i2_5_1__bvfunc11,plain,(
    r2_hidden(c1_5_1__bvfunc11,k1_zfmisc_1(c1_5__bvfunc11)) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_5__bvfunc11,dt_c3_5__bvfunc11,dt_c4_5__bvfunc11,dt_c1_5_1__bvfunc11,dt_c5_5__bvfunc11,dt_c6_5__bvfunc11,e1_5_1__bvfunc11,e3_5__bvfunc11])],[e3_5_1__bvfunc11,i3_5_1__bvfunc11]),
    [interesting(0.65),file(bvfunc11,i2_5_1__bvfunc11),[file(bvfunc11,i2_5_1__bvfunc11)]]).

fof(i1_5_1__bvfunc11,plain,(
    ~ ( r2_hidden(c1_5_1__bvfunc11,k2_tarski(c5_5__bvfunc11,c6_5__bvfunc11))
      & ~ r2_hidden(c1_5_1__bvfunc11,k1_zfmisc_1(c1_5__bvfunc11)) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_5__bvfunc11,dt_c3_5__bvfunc11,dt_c4_5__bvfunc11,dt_c1_5_1__bvfunc11,dt_c5_5__bvfunc11,dt_c6_5__bvfunc11,e3_5__bvfunc11]),discharge_asm(discharge,[e1_5_1__bvfunc11])],[e1_5_1__bvfunc11,i2_5_1__bvfunc11]),
    [interesting(0.65),file(bvfunc11,i1_5_1__bvfunc11),[file(bvfunc11,i1_5_1__bvfunc11)]]).

fof(i1_5_1_tmp__bvfunc11,plain,(
    ~ ( r2_hidden(c1_5_1__bvfunc11,k2_tarski(c5_5__bvfunc11,c6_5__bvfunc11))
      & ~ r2_hidden(c1_5_1__bvfunc11,k1_zfmisc_1(c1_5__bvfunc11)) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_5__bvfunc11,dt_c3_5__bvfunc11,dt_c4_5__bvfunc11,dt_c5_5__bvfunc11,dt_c6_5__bvfunc11,e3_5__bvfunc11]),discharge_asm(discharge,[dt_c1_5_1__bvfunc11])],[dt_c1_5_1__bvfunc11,i1_5_1__bvfunc11]),
    [interesting(0.8),e4_5__bvfunc11]).

fof(e4_5__bvfunc11,plain,(
    r1_tarski(k2_tarski(c5_5__bvfunc11,c6_5__bvfunc11),k1_zfmisc_1(c1_5__bvfunc11)) ),
    inference(let,[status(thm),assumptions([dt_c1_5__bvfunc11,dt_c3_5__bvfunc11,dt_c4_5__bvfunc11,dt_c5_5__bvfunc11,dt_c6_5__bvfunc11,e3_5__bvfunc11])],[i1_5_1_tmp__bvfunc11,commutativity_k2_tarski,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_zfmisc_1,dt_k2_tarski,dt_c1_5__bvfunc11,dt_c5_5__bvfunc11,dt_c6_5__bvfunc11,fc1_subset_1,fc3_subset_1,d3_tarski,dh_c1_5_1__bvfunc11]),
    [interesting(0.8),file(bvfunc11,e4_5__bvfunc11),[file(bvfunc11,e4_5__bvfunc11)]]).

fof(e5_5__bvfunc11,plain,(
    m1_subset_1(k2_tarski(c5_5__bvfunc11,c6_5__bvfunc11),k1_zfmisc_1(k1_zfmisc_1(c1_5__bvfunc11))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5__bvfunc11,dt_c3_5__bvfunc11,dt_c4_5__bvfunc11,dt_c5_5__bvfunc11,dt_c6_5__bvfunc11,e3_5__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,rc1_subset_1,rc2_subset_1,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k2_tarski,reflexivity_r1_tarski,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k2_tarski,dt_m1_subset_1,dt_c1_5__bvfunc11,dt_c5_5__bvfunc11,dt_c6_5__bvfunc11,fc1_subset_1,fc3_subset_1,t3_subset,e4_5__bvfunc11]),
    [interesting(0.8),file(bvfunc11,e5_5__bvfunc11),[file(bvfunc11,e5_5__bvfunc11)]]).

fof(dt_c8_5__bvfunc11,plain,(
    m1_subset_1(c8_5__bvfunc11,k1_zfmisc_1(k1_zfmisc_1(c1_5__bvfunc11))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5__bvfunc11,dt_c3_5__bvfunc11,dt_c4_5__bvfunc11,dt_c5_5__bvfunc11,dt_c6_5__bvfunc11,e3_5__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,rc1_subset_1,rc2_subset_1,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k2_tarski,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k2_tarski,dt_m1_subset_1,dt_c1_5__bvfunc11,dt_c5_5__bvfunc11,dt_c6_5__bvfunc11,fc1_subset_1,fc3_subset_1,t3_subset,de_c8_5__bvfunc11,e5_5__bvfunc11]),
    [interesting(0.8),file(bvfunc11,c8_5__bvfunc11),[file(bvfunc11,c8_5__bvfunc11)]]).

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(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_m1_t_1topsp,axiom,(
    $true ),
    file(t_1topsp,m1_t_1topsp),
    [interesting(0.9),axiom,file(t_1topsp,m1_t_1topsp)]).

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_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_k4_funct_4,axiom,(
    $true ),
    file(funct_4,k4_funct_4),
    [interesting(0.9),axiom,file(funct_4,k4_funct_4)]).

fof(dt_c2_5__bvfunc11,assumption,(
    m1_subset_1(c2_5__bvfunc11,k1_zfmisc_1(k1_bvfunc_2(c1_5__bvfunc11))) ),
    introduced(assumption,[file(bvfunc11,c2_5__bvfunc11)]),
    [interesting(0.8),axiom,file(bvfunc11,c2_5__bvfunc11)]).

fof(fc2_funct_7,theorem,(
    ! [A,B,C,D] : 
      ( ~ v1_xboole_0(k4_funct_4(A,B,C,D))
      & v1_relat_1(k4_funct_4(A,B,C,D))
      & v1_funct_1(k4_funct_4(A,B,C,D)) ) ),
    file(funct_7,fc2_funct_7),
    [interesting(0.9),axiom,file(funct_7,fc2_funct_7)]).

fof(dh_c1_5_2__bvfunc11,definition,
    ( ( r2_hidden(c1_5_2__bvfunc11,c2_5__bvfunc11)
     => r2_hidden(k1_funct_1(k4_funct_4(c3_5__bvfunc11,c4_5__bvfunc11,c5_5__bvfunc11,c6_5__bvfunc11),c1_5_2__bvfunc11),c1_5_2__bvfunc11) )
   => ! [A] : 
        ( r2_hidden(A,c2_5__bvfunc11)
       => r2_hidden(k1_funct_1(k4_funct_4(c3_5__bvfunc11,c4_5__bvfunc11,c5_5__bvfunc11,c6_5__bvfunc11),A),A) ) ),
    introduced(definition,[new_symbol(c1_5_2__bvfunc11),file(bvfunc11,c1_5_2__bvfunc11)]),
    [interesting(0.65),axiom,file(bvfunc11,c1_5_2__bvfunc11)]).

fof(e1_5_2__bvfunc11,assumption,(
    r2_hidden(c1_5_2__bvfunc11,c2_5__bvfunc11) ),
    introduced(assumption,[file(bvfunc11,e1_5_2__bvfunc11)]),
    [interesting(0.65),axiom,file(bvfunc11,e1_5_2__bvfunc11)]).

fof(dt_c1_5_2__bvfunc11,assumption,(
    $true ),
    introduced(assumption,[file(bvfunc11,c1_5_2__bvfunc11)]),
    [interesting(0.65),axiom,file(bvfunc11,c1_5_2__bvfunc11)]).

fof(e2_5_2__bvfunc11,plain,
    ( c1_5_2__bvfunc11 = c3_5__bvfunc11
    | c1_5_2__bvfunc11 = c4_5__bvfunc11 ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5__bvfunc11,dt_c1_5_2__bvfunc11,dt_c2_5__bvfunc11,dt_c3_5__bvfunc11,dt_c4_5__bvfunc11,e1_5_2__bvfunc11,e2_5__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,dt_c1_5__bvfunc11,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,commutativity_k2_tarski,antisymmetry_r2_hidden,dt_k2_tarski,dt_c1_5_2__bvfunc11,dt_c2_5__bvfunc11,dt_c3_5__bvfunc11,dt_c4_5__bvfunc11,fc3_subset_1,t1_subset,t7_boole,e1_5_2__bvfunc11,e2_5__bvfunc11,d2_tarski]),
    [interesting(0.65),file(bvfunc11,e2_5_2__bvfunc11),[file(bvfunc11,e2_5_2__bvfunc11)]]).

fof(t66_funct_4,theorem,(
    ! [A,B,C,D] : 
      ( A != B
     => ( k1_funct_1(k4_funct_4(A,B,C,D),A) = C
        & k1_funct_1(k4_funct_4(A,B,C,D),B) = D ) ) ),
    file(funct_4,t66_funct_4),
    [interesting(0.9),axiom,file(funct_4,t66_funct_4)]).

fof(e3_5_2__bvfunc11,plain,(
    r2_hidden(k1_funct_1(k4_funct_4(c3_5__bvfunc11,c4_5__bvfunc11,c5_5__bvfunc11,c6_5__bvfunc11),c1_5_2__bvfunc11),c1_5_2__bvfunc11) ),
    inference(mizar_by,[status(thm),assumptions([dt_c5_5__bvfunc11,dt_c6_5__bvfunc11,dt_c1_5__bvfunc11,dt_c1_5_2__bvfunc11,dt_c2_5__bvfunc11,dt_c3_5__bvfunc11,dt_c4_5__bvfunc11,e1_5_2__bvfunc11,e2_5__bvfunc11,e3_5__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,dt_c1_5__bvfunc11,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,commutativity_k2_tarski,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k2_tarski,dt_k4_funct_4,dt_c1_5_2__bvfunc11,dt_c2_5__bvfunc11,dt_c3_5__bvfunc11,dt_c4_5__bvfunc11,dt_c5_5__bvfunc11,dt_c6_5__bvfunc11,fc2_funct_7,fc3_subset_1,t1_subset,t7_boole,e2_5_2__bvfunc11,e2_5__bvfunc11,e3_5__bvfunc11,t66_funct_4]),
    [interesting(0.65),file(bvfunc11,e3_5_2__bvfunc11),[file(bvfunc11,e3_5_2__bvfunc11)]]).

fof(i3_5_2__bvfunc11,theorem,(
    $true ),
    introduced(tautology,[file(bvfunc11,i3_5_2__bvfunc11)]),
    [interesting(0.65),trivial,file(bvfunc11,i3_5_2__bvfunc11)]).

fof(i2_5_2__bvfunc11,plain,(
    r2_hidden(k1_funct_1(k4_funct_4(c3_5__bvfunc11,c4_5__bvfunc11,c5_5__bvfunc11,c6_5__bvfunc11),c1_5_2__bvfunc11),c1_5_2__bvfunc11) ),
    inference(conclusion,[status(thm),assumptions([dt_c5_5__bvfunc11,dt_c6_5__bvfunc11,dt_c1_5__bvfunc11,dt_c1_5_2__bvfunc11,dt_c2_5__bvfunc11,dt_c3_5__bvfunc11,dt_c4_5__bvfunc11,e1_5_2__bvfunc11,e2_5__bvfunc11,e3_5__bvfunc11])],[e3_5_2__bvfunc11,i3_5_2__bvfunc11]),
    [interesting(0.65),file(bvfunc11,i2_5_2__bvfunc11),[file(bvfunc11,i2_5_2__bvfunc11)]]).

fof(i1_5_2__bvfunc11,plain,
    ( r2_hidden(c1_5_2__bvfunc11,c2_5__bvfunc11)
   => r2_hidden(k1_funct_1(k4_funct_4(c3_5__bvfunc11,c4_5__bvfunc11,c5_5__bvfunc11,c6_5__bvfunc11),c1_5_2__bvfunc11),c1_5_2__bvfunc11) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c5_5__bvfunc11,dt_c6_5__bvfunc11,dt_c1_5__bvfunc11,dt_c1_5_2__bvfunc11,dt_c2_5__bvfunc11,dt_c3_5__bvfunc11,dt_c4_5__bvfunc11,e2_5__bvfunc11,e3_5__bvfunc11]),discharge_asm(discharge,[e1_5_2__bvfunc11])],[e1_5_2__bvfunc11,i2_5_2__bvfunc11]),
    [interesting(0.65),file(bvfunc11,i1_5_2__bvfunc11),[file(bvfunc11,i1_5_2__bvfunc11)]]).

fof(i1_5_2_tmp__bvfunc11,plain,
    ( r2_hidden(c1_5_2__bvfunc11,c2_5__bvfunc11)
   => r2_hidden(k1_funct_1(k4_funct_4(c3_5__bvfunc11,c4_5__bvfunc11,c5_5__bvfunc11,c6_5__bvfunc11),c1_5_2__bvfunc11),c1_5_2__bvfunc11) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c5_5__bvfunc11,dt_c6_5__bvfunc11,dt_c1_5__bvfunc11,dt_c2_5__bvfunc11,dt_c3_5__bvfunc11,dt_c4_5__bvfunc11,e2_5__bvfunc11,e3_5__bvfunc11]),discharge_asm(discharge,[dt_c1_5_2__bvfunc11])],[dt_c1_5_2__bvfunc11,i1_5_2__bvfunc11]),
    [interesting(0.8),e7_5__bvfunc11]).

fof(e7_5__bvfunc11,plain,(
    ! [A] : 
      ( r2_hidden(A,c2_5__bvfunc11)
     => r2_hidden(k1_funct_1(k4_funct_4(c3_5__bvfunc11,c4_5__bvfunc11,c5_5__bvfunc11,c6_5__bvfunc11),A),A) ) ),
    inference(let,[status(thm),assumptions([dt_c5_5__bvfunc11,dt_c6_5__bvfunc11,dt_c1_5__bvfunc11,dt_c2_5__bvfunc11,dt_c3_5__bvfunc11,dt_c4_5__bvfunc11,e2_5__bvfunc11,e3_5__bvfunc11])],[i1_5_2_tmp__bvfunc11,dh_c1_5_2__bvfunc11]),
    [interesting(0.8),file(bvfunc11,e7_5__bvfunc11),[file(bvfunc11,e7_5__bvfunc11)]]).

fof(t65_funct_4,theorem,(
    ! [A,B,C,D] : 
      ( k1_relat_1(k4_funct_4(A,B,C,D)) = k2_tarski(A,B)
      & r1_tarski(k2_relat_1(k4_funct_4(A,B,C,D)),k2_tarski(C,D)) ) ),
    file(funct_4,t65_funct_4),
    [interesting(0.9),axiom,file(funct_4,t65_funct_4)]).

fof(t67_funct_4,theorem,(
    ! [A,B,C,D] : 
      ( A != B
     => k2_relat_1(k4_funct_4(A,B,C,D)) = k2_tarski(C,D) ) ),
    file(funct_4,t67_funct_4),
    [interesting(0.9),axiom,file(funct_4,t67_funct_4)]).

fof(e6_5__bvfunc11,plain,
    ( k1_relat_1(k4_funct_4(c3_5__bvfunc11,c4_5__bvfunc11,c5_5__bvfunc11,c6_5__bvfunc11)) = k2_tarski(c3_5__bvfunc11,c4_5__bvfunc11)
    & k2_relat_1(k4_funct_4(c3_5__bvfunc11,c4_5__bvfunc11,c5_5__bvfunc11,c6_5__bvfunc11)) = c8_5__bvfunc11 ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_5__bvfunc11,dt_c1_5__bvfunc11,dt_c3_5__bvfunc11,dt_c4_5__bvfunc11,dt_c5_5__bvfunc11,dt_c6_5__bvfunc11,e3_5__bvfunc11,e2_5__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_zfmisc_1,dt_m1_eqrel_1,dt_m1_subset_1,dt_c1_5__bvfunc11,cc1_eqrel_1,cc2_eqrel_1,fc1_subset_1,rc1_subset_1,rc2_subset_1,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k2_tarski,reflexivity_r1_tarski,dt_k1_relat_1,dt_k2_relat_1,dt_k2_tarski,dt_k4_funct_4,dt_c2_5__bvfunc11,dt_c3_5__bvfunc11,dt_c4_5__bvfunc11,dt_c5_5__bvfunc11,dt_c6_5__bvfunc11,dt_c8_5__bvfunc11,de_c8_5__bvfunc11,fc2_funct_7,fc3_subset_1,t3_subset,e2_5__bvfunc11,t65_funct_4,t67_funct_4]),
    [interesting(0.8),file(bvfunc11,e6_5__bvfunc11),[file(bvfunc11,e6_5__bvfunc11)]]).

fof(d5_bvfunc_2,definition,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
         => ( v2_bvfunc_2(B,A)
          <=> ! [C] : 
                ( ( v1_relat_1(C)
                  & v1_funct_1(C) )
               => ! [D] : 
                    ( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(A)))
                   => ~ ( k1_relat_1(C) = B
                        & k2_relat_1(C) = D
                        & ! [E] : 
                            ( r2_hidden(E,B)
                           => r2_hidden(k1_funct_1(C,E),E) )
                        & k8_setfam_1(A,D) = k1_xboole_0 ) ) ) ) ) ) ),
    file(bvfunc_2,d5_bvfunc_2),
    [interesting(0.9),axiom,file(bvfunc_2,d5_bvfunc_2)]).

fof(e8_5__bvfunc11,plain,(
    k8_setfam_1(c1_5__bvfunc11,c8_5__bvfunc11) != k1_xboole_0 ),
    inference(mizar_by,[status(thm),assumptions([e1_5__bvfunc11,dt_c2_5__bvfunc11,dt_c1_5__bvfunc11,dt_c3_5__bvfunc11,dt_c4_5__bvfunc11,dt_c5_5__bvfunc11,dt_c6_5__bvfunc11,e3_5__bvfunc11,e2_5__bvfunc11])],[cc1_funct_7,reflexivity_r1_tarski,existence_m1_eqrel_1,existence_m1_t_1topsp,dt_k1_partit1,dt_m1_eqrel_1,dt_m1_t_1topsp,cc1_eqrel_1,cc2_eqrel_1,cc2_funct_7,rc1_margrel1,commutativity_k2_tarski,antisymmetry_r2_hidden,existence_m1_subset_1,redefinition_k1_bvfunc_2,dt_k1_bvfunc_2,dt_k1_funct_1,dt_k1_relat_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_relat_1,dt_k2_tarski,dt_k4_funct_4,dt_k8_setfam_1,dt_m1_subset_1,dt_c1_5__bvfunc11,dt_c2_5__bvfunc11,dt_c3_5__bvfunc11,dt_c4_5__bvfunc11,dt_c5_5__bvfunc11,dt_c6_5__bvfunc11,dt_c8_5__bvfunc11,de_c8_5__bvfunc11,fc1_margrel1,fc1_subset_1,fc2_funct_7,fc3_funct_7,fc3_subset_1,rc1_subset_1,rc2_subset_1,t1_subset,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole,e7_5__bvfunc11,e1_5__bvfunc11,e2_5__bvfunc11,e6_5__bvfunc11,d5_bvfunc_2]),
    [interesting(0.8),file(bvfunc11,e8_5__bvfunc11),[file(bvfunc11,e8_5__bvfunc11)]]).

fof(t10_mssubfam,theorem,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ! [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(A))
         => ! [D] : 
              ( m1_subset_1(D,k1_zfmisc_1(A))
             => ( B = k2_tarski(C,D)
               => k8_setfam_1(A,B) = k5_subset_1(A,C,D) ) ) ) ) ),
    file(mssubfam,t10_mssubfam),
    [interesting(0.9),axiom,file(mssubfam,t10_mssubfam)]).

fof(e9_5__bvfunc11,plain,(
    k3_xboole_0(c5_5__bvfunc11,c6_5__bvfunc11) != k1_xboole_0 ),
    inference(mizar_by,[status(thm),assumptions([e1_5__bvfunc11,dt_c2_5__bvfunc11,dt_c1_5__bvfunc11,dt_c3_5__bvfunc11,dt_c4_5__bvfunc11,dt_c5_5__bvfunc11,dt_c6_5__bvfunc11,e2_5__bvfunc11,e3_5__bvfunc11])],[cc1_funct_7,reflexivity_r1_tarski,existence_m1_eqrel_1,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,commutativity_k2_tarski,commutativity_k3_xboole_0,idempotence_k3_xboole_0,commutativity_k5_subset_1,idempotence_k5_subset_1,antisymmetry_r2_hidden,existence_m1_subset_1,redefinition_k5_subset_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_tarski,dt_k3_xboole_0,dt_k5_subset_1,dt_k8_setfam_1,dt_m1_subset_1,dt_c1_5__bvfunc11,dt_c3_5__bvfunc11,dt_c4_5__bvfunc11,dt_c5_5__bvfunc11,dt_c6_5__bvfunc11,dt_c8_5__bvfunc11,de_c8_5__bvfunc11,fc1_margrel1,fc1_subset_1,fc3_funct_7,fc3_subset_1,t1_subset,t2_boole,t3_subset,t4_subset,t6_boole,t7_boole,e8_5__bvfunc11,e3_5__bvfunc11,t10_mssubfam]),
    [interesting(0.8),file(bvfunc11,e9_5__bvfunc11),[file(bvfunc11,e9_5__bvfunc11)]]).

fof(i7_5__bvfunc11,theorem,(
    $true ),
    introduced(tautology,[file(bvfunc11,i7_5__bvfunc11)]),
    [interesting(0.8),trivial,file(bvfunc11,i7_5__bvfunc11)]).

fof(i6_5__bvfunc11,plain,(
    ~ r1_xboole_0(c5_5__bvfunc11,c6_5__bvfunc11) ),
    inference(conclusion,[status(thm),assumptions([e1_5__bvfunc11,dt_c2_5__bvfunc11,dt_c1_5__bvfunc11,dt_c3_5__bvfunc11,dt_c4_5__bvfunc11,dt_c5_5__bvfunc11,dt_c6_5__bvfunc11,e2_5__bvfunc11,e3_5__bvfunc11])],[cc1_funct_7,cc2_funct_7,rc1_margrel1,commutativity_k3_xboole_0,idempotence_k3_xboole_0,symmetry_r1_xboole_0,dt_k1_xboole_0,dt_k3_xboole_0,dt_c5_5__bvfunc11,dt_c6_5__bvfunc11,fc1_margrel1,fc3_funct_7,d7_xboole_0,e9_5__bvfunc11,i7_5__bvfunc11]),
    [interesting(0.8),file(bvfunc11,i6_5__bvfunc11),[file(bvfunc11,i6_5__bvfunc11)]]).

fof(i5_5__bvfunc11,plain,(
    ~ ( r2_hidden(c5_5__bvfunc11,c3_5__bvfunc11)
      & r2_hidden(c6_5__bvfunc11,c4_5__bvfunc11)
      & r1_xboole_0(c5_5__bvfunc11,c6_5__bvfunc11) ) ),
    inference(discharge_asm,[status(thm),assumptions([e1_5__bvfunc11,dt_c2_5__bvfunc11,dt_c1_5__bvfunc11,dt_c3_5__bvfunc11,dt_c4_5__bvfunc11,dt_c5_5__bvfunc11,dt_c6_5__bvfunc11,e2_5__bvfunc11]),discharge_asm(discharge,[e3_5__bvfunc11])],[e3_5__bvfunc11,i6_5__bvfunc11]),
    [interesting(0.8),file(bvfunc11,i5_5__bvfunc11),[file(bvfunc11,i5_5__bvfunc11)]]).

fof(i5_5_tmp__bvfunc11,plain,(
    ~ ( r2_hidden(c5_5__bvfunc11,c3_5__bvfunc11)
      & r2_hidden(c6_5__bvfunc11,c4_5__bvfunc11)
      & r1_xboole_0(c5_5__bvfunc11,c6_5__bvfunc11) ) ),
    inference(discharge_asm,[status(thm),assumptions([e1_5__bvfunc11,dt_c2_5__bvfunc11,dt_c1_5__bvfunc11,dt_c3_5__bvfunc11,dt_c4_5__bvfunc11,e2_5__bvfunc11]),discharge_asm(discharge,[dt_c5_5__bvfunc11,dt_c6_5__bvfunc11])],[dt_c5_5__bvfunc11,dt_c6_5__bvfunc11,i5_5__bvfunc11]),
    [interesting(0.8),i4_5__bvfunc11]).

fof(i4_5__bvfunc11,plain,(
    ! [A,B] : 
      ~ ( r2_hidden(A,c3_5__bvfunc11)
        & r2_hidden(B,c4_5__bvfunc11)
        & r1_xboole_0(A,B) ) ),
    inference(let,[status(thm),assumptions([e1_5__bvfunc11,dt_c2_5__bvfunc11,dt_c1_5__bvfunc11,dt_c3_5__bvfunc11,dt_c4_5__bvfunc11,e2_5__bvfunc11])],[i5_5_tmp__bvfunc11,dh_c5_5__bvfunc11,dh_c6_5__bvfunc11]),
    [interesting(0.8),file(bvfunc11,i4_5__bvfunc11),[file(bvfunc11,i4_5__bvfunc11)]]).

fof(i3_5__bvfunc11,plain,
    ( ( v2_bvfunc_2(c2_5__bvfunc11,c1_5__bvfunc11)
      & c2_5__bvfunc11 = k2_tarski(c3_5__bvfunc11,c4_5__bvfunc11) )
   => ( c3_5__bvfunc11 = c4_5__bvfunc11
      | ! [A,B] : 
          ~ ( r2_hidden(A,c3_5__bvfunc11)
            & r2_hidden(B,c4_5__bvfunc11)
            & r1_xboole_0(A,B) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c2_5__bvfunc11,dt_c1_5__bvfunc11,dt_c3_5__bvfunc11,dt_c4_5__bvfunc11]),discharge_asm(discharge,[e1_5__bvfunc11,e2_5__bvfunc11])],[e1_5__bvfunc11,e2_5__bvfunc11,i4_5__bvfunc11]),
    [interesting(0.8),file(bvfunc11,i3_5__bvfunc11),[file(bvfunc11,i3_5__bvfunc11)]]).

fof(i3_5_tmp__bvfunc11,plain,
    ( ( m1_eqrel_1(c3_5__bvfunc11,c1_5__bvfunc11)
      & m1_eqrel_1(c4_5__bvfunc11,c1_5__bvfunc11) )
   => ( ( v2_bvfunc_2(c2_5__bvfunc11,c1_5__bvfunc11)
        & c2_5__bvfunc11 = k2_tarski(c3_5__bvfunc11,c4_5__bvfunc11) )
     => ( c3_5__bvfunc11 = c4_5__bvfunc11
        | ! [A,B] : 
            ~ ( r2_hidden(A,c3_5__bvfunc11)
              & r2_hidden(B,c4_5__bvfunc11)
              & r1_xboole_0(A,B) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c2_5__bvfunc11,dt_c1_5__bvfunc11]),discharge_asm(discharge,[dt_c3_5__bvfunc11,dt_c4_5__bvfunc11])],[dt_c3_5__bvfunc11,dt_c4_5__bvfunc11,i3_5__bvfunc11]),
    [interesting(0.8),i2_5__bvfunc11]).

fof(i2_5__bvfunc11,plain,(
    ! [A] : 
      ( m1_eqrel_1(A,c1_5__bvfunc11)
     => ! [B] : 
          ( m1_eqrel_1(B,c1_5__bvfunc11)
         => ( ( v2_bvfunc_2(c2_5__bvfunc11,c1_5__bvfunc11)
              & c2_5__bvfunc11 = k2_tarski(A,B) )
           => ( A = B
              | ! [C,D] : 
                  ~ ( r2_hidden(C,A)
                    & r2_hidden(D,B)
                    & r1_xboole_0(C,D) ) ) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c2_5__bvfunc11,dt_c1_5__bvfunc11])],[i3_5_tmp__bvfunc11,dh_c3_5__bvfunc11,dh_c4_5__bvfunc11]),
    [interesting(0.8),file(bvfunc11,i2_5__bvfunc11),[file(bvfunc11,i2_5__bvfunc11)]]).

fof(i2_5_tmp__bvfunc11,plain,
    ( m1_subset_1(c2_5__bvfunc11,k1_zfmisc_1(k1_bvfunc_2(c1_5__bvfunc11)))
   => ! [A] : 
        ( m1_eqrel_1(A,c1_5__bvfunc11)
       => ! [B] : 
            ( m1_eqrel_1(B,c1_5__bvfunc11)
           => ( ( v2_bvfunc_2(c2_5__bvfunc11,c1_5__bvfunc11)
                & c2_5__bvfunc11 = k2_tarski(A,B) )
             => ( A = B
                | ! [C,D] : 
                    ~ ( r2_hidden(C,A)
                      & r2_hidden(D,B)
                      & r1_xboole_0(C,D) ) ) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_5__bvfunc11]),discharge_asm(discharge,[dt_c2_5__bvfunc11])],[dt_c2_5__bvfunc11,i2_5__bvfunc11]),
    [interesting(0.8),i1_5__bvfunc11]).

fof(i1_5__bvfunc11,plain,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_bvfunc_2(c1_5__bvfunc11)))
     => ! [B] : 
          ( m1_eqrel_1(B,c1_5__bvfunc11)
         => ! [C] : 
              ( m1_eqrel_1(C,c1_5__bvfunc11)
             => ( ( v2_bvfunc_2(A,c1_5__bvfunc11)
                  & A = k2_tarski(B,C) )
               => ( B = C
                  | ! [D,E] : 
                      ~ ( r2_hidden(D,B)
                        & r2_hidden(E,C)
                        & r1_xboole_0(D,E) ) ) ) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_5__bvfunc11])],[i2_5_tmp__bvfunc11,dh_c2_5__bvfunc11]),
    [interesting(0.8),file(bvfunc11,i1_5__bvfunc11),[file(bvfunc11,i1_5__bvfunc11)]]).

fof(i1_5_tmp__bvfunc11,plain,
    ( ~ v1_xboole_0(c1_5__bvfunc11)
   => ! [A] : 
        ( m1_subset_1(A,k1_zfmisc_1(k1_bvfunc_2(c1_5__bvfunc11)))
       => ! [B] : 
            ( m1_eqrel_1(B,c1_5__bvfunc11)
           => ! [C] : 
                ( m1_eqrel_1(C,c1_5__bvfunc11)
               => ( ( v2_bvfunc_2(A,c1_5__bvfunc11)
                    & A = k2_tarski(B,C) )
                 => ( B = C
                    | ! [D,E] : 
                        ~ ( r2_hidden(D,B)
                          & r2_hidden(E,C)
                          & r1_xboole_0(D,E) ) ) ) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_5__bvfunc11])],[dt_c1_5__bvfunc11,i1_5__bvfunc11]),
    [interesting(1),t5_bvfunc11]).

fof(t5_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)
                 => ( ( v2_bvfunc_2(B,A)
                      & B = k2_tarski(C,D) )
                   => ( C = D
                      | ! [E,F] : 
                          ~ ( r2_hidden(E,C)
                            & r2_hidden(F,D)
                            & r1_xboole_0(E,F) ) ) ) ) ) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_5_tmp__bvfunc11,dh_c1_5__bvfunc11]),
    [interesting(1),file(bvfunc11,t5_bvfunc11),[file(bvfunc11,t5_bvfunc11)]]).