% Mizar ND problem: t1_boolmark,boolmark,33,32 
fof(dh_c1_1__boolmark,definition,
    ( ( ~ v1_xboole_0(c1_1__boolmark)
     => ! [A] : 
          ( ~ v1_xboole_0(A)
         => ! [B] : 
              ( ( v1_funct_1(B)
                & v1_funct_2(B,c1_1__boolmark,A)
                & m2_relset_1(B,c1_1__boolmark,A) )
             => ! [C] : 
                  ( m1_subset_1(C,k1_zfmisc_1(c1_1__boolmark))
                 => ! [D] : 
                      ( m1_subset_1(D,A)
                     => ( v1_funct_1(k1_funct_4(B,k2_funcop_1(C,D)))
                        & v1_funct_2(k1_funct_4(B,k2_funcop_1(C,D)),c1_1__boolmark,A)
                        & m2_relset_1(k1_funct_4(B,k2_funcop_1(C,D)),c1_1__boolmark,A) ) ) ) ) ) )
   => ! [E] : 
        ( ~ v1_xboole_0(E)
       => ! [F] : 
            ( ~ v1_xboole_0(F)
           => ! [G] : 
                ( ( v1_funct_1(G)
                  & v1_funct_2(G,E,F)
                  & m2_relset_1(G,E,F) )
               => ! [H] : 
                    ( m1_subset_1(H,k1_zfmisc_1(E))
                   => ! [I] : 
                        ( m1_subset_1(I,F)
                       => ( v1_funct_1(k1_funct_4(G,k2_funcop_1(H,I)))
                          & v1_funct_2(k1_funct_4(G,k2_funcop_1(H,I)),E,F)
                          & m2_relset_1(k1_funct_4(G,k2_funcop_1(H,I)),E,F) ) ) ) ) ) ) ),
    introduced(definition,[new_symbol(c1_1__boolmark),file(boolmark,c1_1__boolmark)]),
    [interesting(0.8),axiom,file(boolmark,c1_1__boolmark)]).

fof(dh_c2_1__boolmark,definition,
    ( ( ~ v1_xboole_0(c2_1__boolmark)
     => ! [A] : 
          ( ( v1_funct_1(A)
            & v1_funct_2(A,c1_1__boolmark,c2_1__boolmark)
            & m2_relset_1(A,c1_1__boolmark,c2_1__boolmark) )
         => ! [B] : 
              ( m1_subset_1(B,k1_zfmisc_1(c1_1__boolmark))
             => ! [C] : 
                  ( m1_subset_1(C,c2_1__boolmark)
                 => ( v1_funct_1(k1_funct_4(A,k2_funcop_1(B,C)))
                    & v1_funct_2(k1_funct_4(A,k2_funcop_1(B,C)),c1_1__boolmark,c2_1__boolmark)
                    & m2_relset_1(k1_funct_4(A,k2_funcop_1(B,C)),c1_1__boolmark,c2_1__boolmark) ) ) ) ) )
   => ! [D] : 
        ( ~ v1_xboole_0(D)
       => ! [E] : 
            ( ( v1_funct_1(E)
              & v1_funct_2(E,c1_1__boolmark,D)
              & m2_relset_1(E,c1_1__boolmark,D) )
           => ! [F] : 
                ( m1_subset_1(F,k1_zfmisc_1(c1_1__boolmark))
               => ! [G] : 
                    ( m1_subset_1(G,D)
                   => ( v1_funct_1(k1_funct_4(E,k2_funcop_1(F,G)))
                      & v1_funct_2(k1_funct_4(E,k2_funcop_1(F,G)),c1_1__boolmark,D)
                      & m2_relset_1(k1_funct_4(E,k2_funcop_1(F,G)),c1_1__boolmark,D) ) ) ) ) ) ),
    introduced(definition,[new_symbol(c2_1__boolmark),file(boolmark,c2_1__boolmark)]),
    [interesting(0.8),axiom,file(boolmark,c2_1__boolmark)]).

fof(dh_c3_1__boolmark,definition,
    ( ( ( v1_funct_1(c3_1__boolmark)
        & v1_funct_2(c3_1__boolmark,c1_1__boolmark,c2_1__boolmark)
        & m2_relset_1(c3_1__boolmark,c1_1__boolmark,c2_1__boolmark) )
     => ! [A] : 
          ( m1_subset_1(A,k1_zfmisc_1(c1_1__boolmark))
         => ! [B] : 
              ( m1_subset_1(B,c2_1__boolmark)
             => ( v1_funct_1(k1_funct_4(c3_1__boolmark,k2_funcop_1(A,B)))
                & v1_funct_2(k1_funct_4(c3_1__boolmark,k2_funcop_1(A,B)),c1_1__boolmark,c2_1__boolmark)
                & m2_relset_1(k1_funct_4(c3_1__boolmark,k2_funcop_1(A,B)),c1_1__boolmark,c2_1__boolmark) ) ) ) )
   => ! [C] : 
        ( ( v1_funct_1(C)
          & v1_funct_2(C,c1_1__boolmark,c2_1__boolmark)
          & m2_relset_1(C,c1_1__boolmark,c2_1__boolmark) )
       => ! [D] : 
            ( m1_subset_1(D,k1_zfmisc_1(c1_1__boolmark))
           => ! [E] : 
                ( m1_subset_1(E,c2_1__boolmark)
               => ( v1_funct_1(k1_funct_4(C,k2_funcop_1(D,E)))
                  & v1_funct_2(k1_funct_4(C,k2_funcop_1(D,E)),c1_1__boolmark,c2_1__boolmark)
                  & m2_relset_1(k1_funct_4(C,k2_funcop_1(D,E)),c1_1__boolmark,c2_1__boolmark) ) ) ) ) ),
    introduced(definition,[new_symbol(c3_1__boolmark),file(boolmark,c3_1__boolmark)]),
    [interesting(0.8),axiom,file(boolmark,c3_1__boolmark)]).

fof(dh_c4_1__boolmark,definition,
    ( ( m1_subset_1(c4_1__boolmark,k1_zfmisc_1(c1_1__boolmark))
     => ! [A] : 
          ( m1_subset_1(A,c2_1__boolmark)
         => ( v1_funct_1(k1_funct_4(c3_1__boolmark,k2_funcop_1(c4_1__boolmark,A)))
            & v1_funct_2(k1_funct_4(c3_1__boolmark,k2_funcop_1(c4_1__boolmark,A)),c1_1__boolmark,c2_1__boolmark)
            & m2_relset_1(k1_funct_4(c3_1__boolmark,k2_funcop_1(c4_1__boolmark,A)),c1_1__boolmark,c2_1__boolmark) ) ) )
   => ! [B] : 
        ( m1_subset_1(B,k1_zfmisc_1(c1_1__boolmark))
       => ! [C] : 
            ( m1_subset_1(C,c2_1__boolmark)
           => ( v1_funct_1(k1_funct_4(c3_1__boolmark,k2_funcop_1(B,C)))
              & v1_funct_2(k1_funct_4(c3_1__boolmark,k2_funcop_1(B,C)),c1_1__boolmark,c2_1__boolmark)
              & m2_relset_1(k1_funct_4(c3_1__boolmark,k2_funcop_1(B,C)),c1_1__boolmark,c2_1__boolmark) ) ) ) ),
    introduced(definition,[new_symbol(c4_1__boolmark),file(boolmark,c4_1__boolmark)]),
    [interesting(0.8),axiom,file(boolmark,c4_1__boolmark)]).

fof(dh_c5_1__boolmark,definition,
    ( ( m1_subset_1(c5_1__boolmark,c2_1__boolmark)
     => ( v1_funct_1(k1_funct_4(c3_1__boolmark,k2_funcop_1(c4_1__boolmark,c5_1__boolmark)))
        & v1_funct_2(k1_funct_4(c3_1__boolmark,k2_funcop_1(c4_1__boolmark,c5_1__boolmark)),c1_1__boolmark,c2_1__boolmark)
        & m2_relset_1(k1_funct_4(c3_1__boolmark,k2_funcop_1(c4_1__boolmark,c5_1__boolmark)),c1_1__boolmark,c2_1__boolmark) ) )
   => ! [A] : 
        ( m1_subset_1(A,c2_1__boolmark)
       => ( v1_funct_1(k1_funct_4(c3_1__boolmark,k2_funcop_1(c4_1__boolmark,A)))
          & v1_funct_2(k1_funct_4(c3_1__boolmark,k2_funcop_1(c4_1__boolmark,A)),c1_1__boolmark,c2_1__boolmark)
          & m2_relset_1(k1_funct_4(c3_1__boolmark,k2_funcop_1(c4_1__boolmark,A)),c1_1__boolmark,c2_1__boolmark) ) ) ),
    introduced(definition,[new_symbol(c5_1__boolmark),file(boolmark,c5_1__boolmark)]),
    [interesting(0.8),axiom,file(boolmark,c5_1__boolmark)]).

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(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_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m1_relset_1(C,A,B) ),
    file(relset_1,m1_relset_1),
    [interesting(0.9),axiom,file(relset_1,m1_relset_1)]).

fof(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(dt_k1_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k1_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,k1_zfmisc_1)]).

fof(dt_k2_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k2_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,k2_zfmisc_1)]).

fof(dt_m1_relset_1,axiom,(
    $true ),
    file(relset_1,m1_relset_1),
    [interesting(0.9),axiom,file(relset_1,m1_relset_1)]).

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

fof(cc1_finseq_1,theorem,(
    ! [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) ) ) ),
    file(finseq_1,cc1_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,cc1_finseq_1)]).

fof(cc1_relset_1,theorem,(
    ! [A,B,C] : 
      ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
     => v1_relat_1(C) ) ),
    file(relset_1,cc1_relset_1),
    [interesting(0.9),axiom,file(relset_1,cc1_relset_1)]).

fof(fc11_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_finset_1(A) )
     => v1_finset_1(k2_relat_1(A)) ) ),
    file(finseq_1,fc11_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,fc11_finseq_1)]).

fof(fc17_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finset_1(A) )
     => v1_finset_1(k1_relat_1(A)) ) ),
    file(finseq_1,fc17_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,fc17_finseq_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(fc3_funcop_1,theorem,(
    ! [A,B] : 
      ( v1_xboole_0(B)
     => ( v1_xboole_0(k2_funcop_1(B,A))
        & v1_relat_1(k2_funcop_1(B,A))
        & v1_funct_1(k2_funcop_1(B,A))
        & v2_funct_1(k2_funcop_1(B,A)) ) ) ),
    file(funcop_1,fc3_funcop_1),
    [interesting(0.9),axiom,file(funcop_1,fc3_funcop_1)]).

fof(fc4_subset_1,theorem,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ~ v1_xboole_0(k2_zfmisc_1(A,B)) ) ),
    file(subset_1,fc4_subset_1),
    [interesting(0.9),axiom,file(subset_1,fc4_subset_1)]).

fof(fc9_funcop_1,theorem,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => ( v1_relat_1(k2_funcop_1(A,B))
        & v2_relat_1(k2_funcop_1(A,B))
        & v1_funct_1(k2_funcop_1(A,B)) ) ) ),
    file(funcop_1,fc9_funcop_1),
    [interesting(0.9),axiom,file(funcop_1,fc9_funcop_1)]).

fof(rc1_finseq_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finseq_1(A) ) ),
    file(finseq_1,rc1_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,rc1_finseq_1)]).

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

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(rc3_finseq_1,theorem,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_finset_1(A)
      & v1_finseq_1(A) ) ),
    file(finseq_1,rc3_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,rc3_finseq_1)]).

fof(rc6_finseq_1,theorem,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_finset_1(A) ) ),
    file(finseq_1,rc6_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,rc6_finseq_1)]).

fof(rc7_finseq_1,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A) ) ),
    file(finseq_1,rc7_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,rc7_finseq_1)]).

fof(rc8_finseq_1,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A)
      & v1_finseq_1(A) ) ),
    file(finseq_1,rc8_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,rc8_finseq_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(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(idempotence_k1_funct_4,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B) )
     => k1_funct_4(A,A) = A ) ),
    file(funct_4,k1_funct_4),
    [interesting(0.9),axiom,file(funct_4,k1_funct_4)]).

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_m2_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m2_relset_1(C,A,B) ),
    file(relset_1,m2_relset_1),
    [interesting(0.9),axiom,file(relset_1,m2_relset_1)]).

fof(redefinition_k4_relset_1,definition,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => k4_relset_1(A,B,C) = k1_relat_1(C) ) ),
    file(relset_1,k4_relset_1),
    [interesting(0.9),axiom,file(relset_1,k4_relset_1)]).

fof(redefinition_m2_relset_1,definition,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
    <=> m1_relset_1(C,A,B) ) ),
    file(relset_1,m2_relset_1),
    [interesting(0.9),axiom,file(relset_1,m2_relset_1)]).

fof(dt_k1_funct_4,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B) )
     => ( v1_relat_1(k1_funct_4(A,B))
        & v1_funct_1(k1_funct_4(A,B)) ) ) ),
    file(funct_4,k1_funct_4),
    [interesting(0.9),axiom,file(funct_4,k1_funct_4)]).

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_k1_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k1_xboole_0)]).

fof(dt_k2_funcop_1,axiom,(
    $true ),
    file(funcop_1,k2_funcop_1),
    [interesting(0.9),axiom,file(funcop_1,k2_funcop_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_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => m1_subset_1(k4_relset_1(A,B,C),k1_zfmisc_1(A)) ) ),
    file(relset_1,k4_relset_1),
    [interesting(0.9),axiom,file(relset_1,k4_relset_1)]).

fof(dt_m2_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ),
    file(relset_1,m2_relset_1),
    [interesting(0.9),axiom,file(relset_1,m2_relset_1)]).

fof(dt_c1_1__boolmark,assumption,(
    ~ v1_xboole_0(c1_1__boolmark) ),
    introduced(assumption,[file(boolmark,c1_1__boolmark)]),
    [interesting(0.8),axiom,file(boolmark,c1_1__boolmark)]).

fof(dt_c2_1__boolmark,assumption,(
    ~ v1_xboole_0(c2_1__boolmark) ),
    introduced(assumption,[file(boolmark,c2_1__boolmark)]),
    [interesting(0.8),axiom,file(boolmark,c2_1__boolmark)]).

fof(dt_c3_1__boolmark,assumption,
    ( v1_funct_1(c3_1__boolmark)
    & v1_funct_2(c3_1__boolmark,c1_1__boolmark,c2_1__boolmark)
    & m2_relset_1(c3_1__boolmark,c1_1__boolmark,c2_1__boolmark) ),
    introduced(assumption,[file(boolmark,c3_1__boolmark)]),
    [interesting(0.8),axiom,file(boolmark,c3_1__boolmark)]).

fof(dt_c4_1__boolmark,assumption,(
    m1_subset_1(c4_1__boolmark,k1_zfmisc_1(c1_1__boolmark)) ),
    introduced(assumption,[file(boolmark,c4_1__boolmark)]),
    [interesting(0.8),axiom,file(boolmark,c4_1__boolmark)]).

fof(dt_c5_1__boolmark,assumption,(
    m1_subset_1(c5_1__boolmark,c2_1__boolmark) ),
    introduced(assumption,[file(boolmark,c5_1__boolmark)]),
    [interesting(0.8),axiom,file(boolmark,c5_1__boolmark)]).

fof(fc1_funcop_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(k2_funcop_1(A,B))
      & v1_funct_1(k2_funcop_1(A,B)) ) ),
    file(funcop_1,fc1_funcop_1),
    [interesting(0.9),axiom,file(funcop_1,fc1_funcop_1)]).

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

fof(fc2_finseq_1,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) ),
    file(finseq_1,fc2_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,fc2_finseq_1)]).

fof(fc2_funcop_1,theorem,(
    ! [A] : 
      ( v1_xboole_0(k2_funcop_1(k1_xboole_0,A))
      & v1_relat_1(k2_funcop_1(k1_xboole_0,A))
      & v1_funct_1(k2_funcop_1(k1_xboole_0,A))
      & v2_funct_1(k2_funcop_1(k1_xboole_0,A)) ) ),
    file(funcop_1,fc2_funcop_1),
    [interesting(0.9),axiom,file(funcop_1,fc2_funcop_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(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(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(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(redefinition_k6_domain_1,definition,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A) )
     => k6_domain_1(A,B) = k1_tarski(B) ) ),
    file(domain_1,k6_domain_1),
    [interesting(0.9),axiom,file(domain_1,k6_domain_1)]).

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

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_k6_domain_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A) )
     => m1_subset_1(k6_domain_1(A,B),k1_zfmisc_1(A)) ) ),
    file(domain_1,k6_domain_1),
    [interesting(0.9),axiom,file(domain_1,k6_domain_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(t18_funct_4,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => r1_tarski(k2_relat_1(k1_funct_4(A,B)),k2_xboole_0(k2_relat_1(A),k2_relat_1(B))) ) ) ),
    file(funct_4,t18_funct_4),
    [interesting(0.9),axiom,file(funct_4,t18_funct_4)]).

fof(e6_1__boolmark,plain,(
    r1_tarski(k2_relat_1(k1_funct_4(c3_1__boolmark,k2_funcop_1(c4_1__boolmark,c5_1__boolmark))),k2_xboole_0(k2_relat_1(c3_1__boolmark),k2_relat_1(k2_funcop_1(c4_1__boolmark,c5_1__boolmark)))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_1__boolmark,dt_c2_1__boolmark,dt_c3_1__boolmark,dt_c4_1__boolmark,dt_c5_1__boolmark])],[cc1_finseq_1,fc11_finseq_1,rc1_finseq_1,rc1_margrel1,rc3_finseq_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,antisymmetry_r2_hidden,dt_k1_xboole_0,fc1_margrel1,fc2_finseq_1,fc2_funcop_1,t1_boole,t1_subset,t4_subset,t5_subset,existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc3_funcop_1,fc4_subset_1,fc9_funcop_1,rc1_subset_1,rc2_subset_1,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_zfmisc_1,dt_m1_subset_1,dt_m2_relset_1,dt_c1_1__boolmark,dt_c2_1__boolmark,fc1_subset_1,idempotence_k1_funct_4,commutativity_k2_xboole_0,idempotence_k2_xboole_0,reflexivity_r1_tarski,dt_k1_funct_4,dt_k2_funcop_1,dt_k2_relat_1,dt_k2_xboole_0,dt_c3_1__boolmark,dt_c4_1__boolmark,dt_c5_1__boolmark,fc1_funcop_1,t3_subset,t18_funct_4]),
    [interesting(0.8),file(boolmark,e6_1__boolmark),[file(boolmark,e6_1__boolmark)]]).

fof(t19_funcop_1,theorem,(
    ! [A,B] : 
      ( k1_relat_1(k2_funcop_1(A,B)) = A
      & r1_tarski(k2_relat_1(k2_funcop_1(A,B)),k1_tarski(B)) ) ),
    file(funcop_1,t19_funcop_1),
    [interesting(0.9),axiom,file(funcop_1,t19_funcop_1)]).

fof(e4_1__boolmark,plain,(
    r1_tarski(k2_relat_1(k2_funcop_1(c4_1__boolmark,c5_1__boolmark)),k6_domain_1(c2_1__boolmark,c5_1__boolmark)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_1__boolmark,dt_c2_1__boolmark,dt_c4_1__boolmark,dt_c5_1__boolmark])],[cc1_finseq_1,fc11_finseq_1,fc17_finseq_1,rc1_finseq_1,rc1_margrel1,rc3_finseq_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,antisymmetry_r2_hidden,dt_k1_xboole_0,fc1_margrel1,fc2_finseq_1,fc2_funcop_1,t1_subset,t4_subset,t5_subset,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,dt_c1_1__boolmark,fc1_subset_1,fc3_funcop_1,fc9_funcop_1,rc1_subset_1,rc2_subset_1,t2_subset,t6_boole,t7_boole,t8_boole,reflexivity_r1_tarski,redefinition_k6_domain_1,dt_k1_relat_1,dt_k1_tarski,dt_k2_funcop_1,dt_k2_relat_1,dt_k6_domain_1,dt_c2_1__boolmark,dt_c4_1__boolmark,dt_c5_1__boolmark,fc1_funcop_1,fc2_subset_1,t3_subset,t19_funcop_1]),
    [interesting(0.8),file(boolmark,e4_1__boolmark),[file(boolmark,e4_1__boolmark)]]).

fof(t12_relset_1,theorem,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => ( r1_tarski(k1_relat_1(C),A)
        & r1_tarski(k2_relat_1(C),B) ) ) ),
    file(relset_1,t12_relset_1),
    [interesting(0.9),axiom,file(relset_1,t12_relset_1)]).

fof(e3_1__boolmark,plain,(
    r1_tarski(k2_relat_1(c3_1__boolmark),c2_1__boolmark) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_1__boolmark,dt_c2_1__boolmark,dt_c3_1__boolmark])],[cc1_finseq_1,fc11_finseq_1,fc17_finseq_1,rc1_finseq_1,rc1_margrel1,rc3_finseq_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,antisymmetry_r2_hidden,dt_k1_xboole_0,fc1_margrel1,fc2_finseq_1,t1_subset,t4_subset,t5_subset,t8_boole,existence_m1_relset_1,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_m1_relset_1,dt_m1_subset_1,dt_c1_1__boolmark,cc1_relset_1,fc1_subset_1,fc4_subset_1,rc1_subset_1,rc2_subset_1,t2_subset,t6_boole,t7_boole,reflexivity_r1_tarski,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_relat_1,dt_k2_relat_1,dt_m2_relset_1,dt_c2_1__boolmark,dt_c3_1__boolmark,t3_subset,t12_relset_1]),
    [interesting(0.8),file(boolmark,e3_1__boolmark),[file(boolmark,e3_1__boolmark)]]).

fof(t13_xboole_1,theorem,(
    ! [A,B,C,D] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(C,D) )
     => r1_tarski(k2_xboole_0(A,C),k2_xboole_0(B,D)) ) ),
    file(xboole_1,t13_xboole_1),
    [interesting(0.9),axiom,file(xboole_1,t13_xboole_1)]).

fof(e5_1__boolmark,plain,(
    r1_tarski(k2_xboole_0(k2_relat_1(c3_1__boolmark),k2_relat_1(k2_funcop_1(c4_1__boolmark,c5_1__boolmark))),k2_xboole_0(c2_1__boolmark,k6_domain_1(c2_1__boolmark,c5_1__boolmark))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c4_1__boolmark,dt_c5_1__boolmark,dt_c1_1__boolmark,dt_c2_1__boolmark,dt_c3_1__boolmark])],[cc1_finseq_1,fc11_finseq_1,rc1_finseq_1,rc1_margrel1,rc3_finseq_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,antisymmetry_r2_hidden,existence_m1_relset_1,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc1_margrel1,fc2_finseq_1,fc2_funcop_1,fc4_subset_1,t1_boole,t1_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_tarski,dt_k1_zfmisc_1,dt_m1_subset_1,dt_m2_relset_1,dt_c1_1__boolmark,fc1_subset_1,fc2_subset_1,fc3_funcop_1,fc9_funcop_1,rc1_subset_1,rc2_subset_1,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,reflexivity_r1_tarski,redefinition_k6_domain_1,dt_k2_funcop_1,dt_k2_relat_1,dt_k2_xboole_0,dt_k6_domain_1,dt_c2_1__boolmark,dt_c3_1__boolmark,dt_c4_1__boolmark,dt_c5_1__boolmark,fc1_funcop_1,t3_subset,e4_1__boolmark,e3_1__boolmark,t13_xboole_1]),
    [interesting(0.8),file(boolmark,e5_1__boolmark),[file(boolmark,e5_1__boolmark)]]).

fof(t1_xboole_1,theorem,(
    ! [A,B,C] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(B,C) )
     => r1_tarski(A,C) ) ),
    file(xboole_1,t1_xboole_1),
    [interesting(0.9),axiom,file(xboole_1,t1_xboole_1)]).

fof(e7_1__boolmark,plain,(
    r1_tarski(k2_relat_1(k1_funct_4(c3_1__boolmark,k2_funcop_1(c4_1__boolmark,c5_1__boolmark))),k2_xboole_0(c2_1__boolmark,k6_domain_1(c2_1__boolmark,c5_1__boolmark))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c4_1__boolmark,dt_c5_1__boolmark,dt_c1_1__boolmark,dt_c2_1__boolmark,dt_c3_1__boolmark])],[cc1_finseq_1,fc11_finseq_1,rc1_finseq_1,rc1_margrel1,rc3_finseq_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,antisymmetry_r2_hidden,existence_m1_relset_1,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc1_margrel1,fc2_finseq_1,fc2_funcop_1,fc4_subset_1,t1_boole,t1_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_tarski,dt_k1_zfmisc_1,dt_m1_subset_1,dt_m2_relset_1,dt_c1_1__boolmark,fc1_subset_1,fc2_subset_1,fc3_funcop_1,fc9_funcop_1,rc1_subset_1,rc2_subset_1,t2_subset,t6_boole,t7_boole,t8_boole,idempotence_k1_funct_4,commutativity_k2_xboole_0,idempotence_k2_xboole_0,reflexivity_r1_tarski,redefinition_k6_domain_1,dt_k1_funct_4,dt_k2_funcop_1,dt_k2_relat_1,dt_k2_xboole_0,dt_k6_domain_1,dt_c2_1__boolmark,dt_c3_1__boolmark,dt_c4_1__boolmark,dt_c5_1__boolmark,fc1_funcop_1,t3_subset,e6_1__boolmark,e5_1__boolmark,t1_xboole_1]),
    [interesting(0.8),file(boolmark,e7_1__boolmark),[file(boolmark,e7_1__boolmark)]]).

fof(t46_zfmisc_1,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => k2_xboole_0(k1_tarski(A),B) = B ) ),
    file(zfmisc_1,t46_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,t46_zfmisc_1)]).

fof(e8_1__boolmark,plain,(
    r1_tarski(k2_relat_1(k1_funct_4(c3_1__boolmark,k2_funcop_1(c4_1__boolmark,c5_1__boolmark))),c2_1__boolmark) ),
    inference(mizar_by,[status(thm),assumptions([dt_c4_1__boolmark,dt_c5_1__boolmark,dt_c1_1__boolmark,dt_c2_1__boolmark,dt_c3_1__boolmark])],[cc1_finseq_1,fc11_finseq_1,rc1_finseq_1,rc1_margrel1,rc3_finseq_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,existence_m1_relset_1,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc1_margrel1,fc2_finseq_1,fc2_funcop_1,fc4_subset_1,t1_boole,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_zfmisc_1,dt_m1_subset_1,dt_m2_relset_1,dt_c1_1__boolmark,fc1_subset_1,fc3_funcop_1,fc9_funcop_1,rc1_subset_1,rc2_subset_1,t2_subset,t4_subset,t5_subset,t6_boole,t8_boole,idempotence_k1_funct_4,commutativity_k2_xboole_0,idempotence_k2_xboole_0,reflexivity_r1_tarski,antisymmetry_r2_hidden,redefinition_k6_domain_1,dt_k1_funct_4,dt_k1_tarski,dt_k2_funcop_1,dt_k2_relat_1,dt_k2_xboole_0,dt_k6_domain_1,dt_c2_1__boolmark,dt_c3_1__boolmark,dt_c4_1__boolmark,dt_c5_1__boolmark,fc1_funcop_1,fc2_subset_1,t1_subset,t3_subset,t7_boole,e7_1__boolmark,t46_zfmisc_1]),
    [interesting(0.8),file(boolmark,e8_1__boolmark),[file(boolmark,e8_1__boolmark)]]).

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

fof(d1_funct_4,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( C = k1_funct_4(A,B)
              <=> ( k1_relat_1(C) = k2_xboole_0(k1_relat_1(A),k1_relat_1(B))
                  & ! [D] : 
                      ( r2_hidden(D,k2_xboole_0(k1_relat_1(A),k1_relat_1(B)))
                     => ( ( r2_hidden(D,k1_relat_1(B))
                         => k1_funct_1(C,D) = k1_funct_1(B,D) )
                        & ( ~ r2_hidden(D,k1_relat_1(B))
                         => k1_funct_1(C,D) = k1_funct_1(A,D) ) ) ) ) ) ) ) ) ),
    file(funct_4,d1_funct_4),
    [interesting(0.9),axiom,file(funct_4,d1_funct_4)]).

fof(e1_1_1__boolmark,plain,(
    k1_relat_1(k1_funct_4(c3_1__boolmark,k2_funcop_1(c4_1__boolmark,c5_1__boolmark))) = k2_xboole_0(k1_relat_1(c3_1__boolmark),k1_relat_1(k2_funcop_1(c4_1__boolmark,c5_1__boolmark))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_1__boolmark,dt_c2_1__boolmark,dt_c3_1__boolmark,dt_c4_1__boolmark,dt_c5_1__boolmark])],[cc1_finseq_1,fc17_finseq_1,rc1_finseq_1,rc1_margrel1,rc3_finseq_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,reflexivity_r1_tarski,existence_m1_relset_1,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc1_margrel1,fc2_finseq_1,fc2_funcop_1,fc4_subset_1,t1_boole,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_zfmisc_1,dt_m1_subset_1,dt_m2_relset_1,dt_c1_1__boolmark,dt_c2_1__boolmark,fc1_subset_1,fc3_funcop_1,fc9_funcop_1,rc1_subset_1,rc2_subset_1,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,idempotence_k1_funct_4,commutativity_k2_xboole_0,idempotence_k2_xboole_0,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_funct_4,dt_k1_relat_1,dt_k2_funcop_1,dt_k2_xboole_0,dt_c3_1__boolmark,dt_c4_1__boolmark,dt_c5_1__boolmark,fc1_funcop_1,t1_subset,t7_boole,d1_funct_4]),
    [interesting(0.65),file(boolmark,e1_1_1__boolmark),[file(boolmark,e1_1_1__boolmark)]]).

fof(d1_funct_2,definition,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => ( ( ( B = k1_xboole_0
           => A = k1_xboole_0 )
         => ( v1_funct_2(C,A,B)
          <=> A = k4_relset_1(A,B,C) ) )
        & ( B = k1_xboole_0
         => ( A = k1_xboole_0
            | ( v1_funct_2(C,A,B)
            <=> C = k1_xboole_0 ) ) ) ) ) ),
    file(funct_2,d1_funct_2),
    [interesting(0.9),axiom,file(funct_2,d1_funct_2)]).

fof(e1_1__boolmark,plain,(
    k1_relat_1(c3_1__boolmark) = c1_1__boolmark ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_1__boolmark,dt_c1_1__boolmark,dt_c3_1__boolmark])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,t1_subset,t4_subset,t5_subset,existence_m1_relset_1,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_m1_relset_1,dt_m1_subset_1,dt_c2_1__boolmark,cc1_finseq_1,cc1_relset_1,fc17_finseq_1,fc1_subset_1,fc4_subset_1,rc1_finseq_1,rc1_margrel1,rc1_subset_1,rc2_subset_1,rc3_finseq_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t3_subset,t7_boole,t8_boole,existence_m2_relset_1,redefinition_k4_relset_1,redefinition_m2_relset_1,dt_k1_relat_1,dt_k1_xboole_0,dt_k4_relset_1,dt_m2_relset_1,dt_c1_1__boolmark,dt_c3_1__boolmark,fc1_margrel1,fc2_finseq_1,t6_boole,d1_funct_2]),
    [interesting(0.8),file(boolmark,e1_1__boolmark),[file(boolmark,e1_1__boolmark)]]).

fof(e2_1_1__boolmark,plain,(
    k2_xboole_0(k1_relat_1(c3_1__boolmark),k1_relat_1(k2_funcop_1(c4_1__boolmark,c5_1__boolmark))) = k2_xboole_0(c1_1__boolmark,c4_1__boolmark) ),
    inference(mizar_by,[status(thm),assumptions([dt_c4_1__boolmark,dt_c5_1__boolmark,dt_c2_1__boolmark,dt_c1_1__boolmark,dt_c3_1__boolmark])],[cc1_finseq_1,fc11_finseq_1,fc17_finseq_1,rc1_finseq_1,rc1_margrel1,rc3_finseq_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,antisymmetry_r2_hidden,existence_m1_relset_1,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc1_margrel1,fc2_finseq_1,fc2_funcop_1,fc4_subset_1,t1_boole,t1_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_zfmisc_1,dt_m1_subset_1,dt_m2_relset_1,dt_c2_1__boolmark,fc1_subset_1,fc3_funcop_1,fc9_funcop_1,rc1_subset_1,rc2_subset_1,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,reflexivity_r1_tarski,dt_k1_relat_1,dt_k1_tarski,dt_k2_funcop_1,dt_k2_relat_1,dt_k2_xboole_0,dt_c1_1__boolmark,dt_c3_1__boolmark,dt_c4_1__boolmark,dt_c5_1__boolmark,fc1_funcop_1,fc2_subset_1,t3_subset,e1_1__boolmark,t19_funcop_1]),
    [interesting(0.65),file(boolmark,e2_1_1__boolmark),[file(boolmark,e2_1_1__boolmark)]]).

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(dt_k2_subset_1,axiom,(
    ! [A] : m1_subset_1(k2_subset_1(A),k1_zfmisc_1(A)) ),
    file(subset_1,k2_subset_1),
    [interesting(0.9),axiom,file(subset_1,k2_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(d4_subset_1,definition,(
    ! [A] : k2_subset_1(A) = A ),
    file(subset_1,d4_subset_1),
    [interesting(0.9),axiom,file(subset_1,d4_subset_1)]).

fof(e3_1_1__boolmark,plain,(
    k2_xboole_0(c1_1__boolmark,c4_1__boolmark) = k4_subset_1(c1_1__boolmark,k2_subset_1(c1_1__boolmark),c4_1__boolmark) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_1__boolmark,dt_c4_1__boolmark])],[cc1_finseq_1,rc1_finseq_1,rc1_margrel1,rc3_finseq_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,fc1_margrel1,fc2_finseq_1,t1_boole,t1_subset,t4_subset,t5_subset,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,fc1_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_k4_subset_1,dt_k2_subset_1,dt_k2_xboole_0,dt_k4_subset_1,dt_c1_1__boolmark,dt_c4_1__boolmark,d4_subset_1]),
    [interesting(0.65),file(boolmark,e3_1_1__boolmark),[file(boolmark,e3_1_1__boolmark)]]).

fof(t28_subset_1,theorem,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
     => k4_subset_1(A,B,k2_subset_1(A)) = k2_subset_1(A) ) ),
    file(subset_1,t28_subset_1),
    [interesting(0.9),axiom,file(subset_1,t28_subset_1)]).

fof(e4_1_1__boolmark,plain,(
    k4_subset_1(c1_1__boolmark,k2_subset_1(c1_1__boolmark),c4_1__boolmark) = k2_subset_1(c1_1__boolmark) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_1__boolmark,dt_c4_1__boolmark])],[cc1_finseq_1,rc1_finseq_1,rc1_margrel1,rc3_finseq_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,antisymmetry_r2_hidden,dt_k1_xboole_0,fc1_margrel1,fc2_finseq_1,t1_boole,t1_subset,t4_subset,t5_subset,commutativity_k2_xboole_0,idempotence_k2_xboole_0,reflexivity_r1_tarski,dt_k2_xboole_0,rc1_subset_1,rc2_subset_1,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k4_subset_1,idempotence_k4_subset_1,existence_m1_subset_1,redefinition_k4_subset_1,dt_k1_zfmisc_1,dt_k2_subset_1,dt_k4_subset_1,dt_m1_subset_1,dt_c1_1__boolmark,dt_c4_1__boolmark,fc1_subset_1,t3_subset,t28_subset_1]),
    [interesting(0.65),file(boolmark,e4_1_1__boolmark),[file(boolmark,e4_1_1__boolmark)]]).

fof(e5_1_1__boolmark,plain,(
    k2_subset_1(c1_1__boolmark) = c1_1__boolmark ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_1__boolmark])],[cc1_finseq_1,rc1_finseq_1,rc1_margrel1,rc3_finseq_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,fc1_margrel1,fc2_finseq_1,t1_subset,t4_subset,t5_subset,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,fc1_subset_1,rc1_subset_1,rc2_subset_1,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,dt_k2_subset_1,dt_c1_1__boolmark,d4_subset_1]),
    [interesting(0.65),file(boolmark,e5_1_1__boolmark),[file(boolmark,e5_1_1__boolmark)]]).

fof(e2_1__boolmark,plain,(
    k1_relat_1(k1_funct_4(c3_1__boolmark,k2_funcop_1(c4_1__boolmark,c5_1__boolmark))) = c1_1__boolmark ),
    inference(iterative_eq,[status(thm),assumptions([dt_c5_1__boolmark,dt_c2_1__boolmark,dt_c3_1__boolmark,dt_c4_1__boolmark,dt_c1_1__boolmark])],[e1_1_1__boolmark,e2_1_1__boolmark,e3_1_1__boolmark,e4_1_1__boolmark,e5_1_1__boolmark]),
    [interesting(0.8),file(boolmark,e2_1__boolmark),[file(boolmark,e2_1__boolmark)]]).

fof(t11_relset_1,theorem,(
    ! [A,B,C] : 
      ( v1_relat_1(C)
     => ( ( r1_tarski(k1_relat_1(C),A)
          & r1_tarski(k2_relat_1(C),B) )
       => m2_relset_1(C,A,B) ) ) ),
    file(relset_1,t11_relset_1),
    [interesting(0.9),axiom,file(relset_1,t11_relset_1)]).

fof(e9_1__boolmark,plain,
    ( v1_funct_1(k1_funct_4(c3_1__boolmark,k2_funcop_1(c4_1__boolmark,c5_1__boolmark)))
    & v1_funct_2(k1_funct_4(c3_1__boolmark,k2_funcop_1(c4_1__boolmark,c5_1__boolmark)),c1_1__boolmark,c2_1__boolmark)
    & m2_relset_1(k1_funct_4(c3_1__boolmark,k2_funcop_1(c4_1__boolmark,c5_1__boolmark)),c1_1__boolmark,c2_1__boolmark) ),
    inference(mizar_by,[status(thm),assumptions([dt_c5_1__boolmark,dt_c2_1__boolmark,dt_c3_1__boolmark,dt_c4_1__boolmark,dt_c1_1__boolmark])],[antisymmetry_r2_hidden,t1_subset,t4_subset,t5_subset,existence_m1_relset_1,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_m1_relset_1,dt_m1_subset_1,cc1_finseq_1,cc1_relset_1,fc11_finseq_1,fc17_finseq_1,fc1_subset_1,fc3_funcop_1,fc4_subset_1,fc9_funcop_1,rc1_finseq_1,rc1_margrel1,rc1_subset_1,rc2_subset_1,rc3_finseq_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t7_boole,t8_boole,idempotence_k1_funct_4,reflexivity_r1_tarski,existence_m2_relset_1,redefinition_k4_relset_1,redefinition_m2_relset_1,dt_k1_funct_4,dt_k1_relat_1,dt_k1_xboole_0,dt_k2_funcop_1,dt_k2_relat_1,dt_k4_relset_1,dt_m2_relset_1,dt_c1_1__boolmark,dt_c2_1__boolmark,dt_c3_1__boolmark,dt_c4_1__boolmark,dt_c5_1__boolmark,fc1_funcop_1,fc1_margrel1,fc2_finseq_1,fc2_funcop_1,t3_subset,t6_boole,e8_1__boolmark,e2_1__boolmark,d1_funct_2,t11_relset_1]),
    [interesting(0.8),file(boolmark,e9_1__boolmark),[file(boolmark,e9_1__boolmark)]]).

fof(i5_1__boolmark,theorem,(
    $true ),
    introduced(tautology,[file(boolmark,i5_1__boolmark)]),
    [interesting(0.8),trivial,file(boolmark,i5_1__boolmark)]).

fof(i4_1__boolmark,plain,
    ( v1_funct_1(k1_funct_4(c3_1__boolmark,k2_funcop_1(c4_1__boolmark,c5_1__boolmark)))
    & v1_funct_2(k1_funct_4(c3_1__boolmark,k2_funcop_1(c4_1__boolmark,c5_1__boolmark)),c1_1__boolmark,c2_1__boolmark)
    & m2_relset_1(k1_funct_4(c3_1__boolmark,k2_funcop_1(c4_1__boolmark,c5_1__boolmark)),c1_1__boolmark,c2_1__boolmark) ),
    inference(conclusion,[status(thm),assumptions([dt_c5_1__boolmark,dt_c2_1__boolmark,dt_c3_1__boolmark,dt_c4_1__boolmark,dt_c1_1__boolmark])],[e9_1__boolmark,i5_1__boolmark]),
    [interesting(0.8),file(boolmark,i4_1__boolmark),[file(boolmark,i4_1__boolmark)]]).

fof(i4_1_tmp__boolmark,plain,
    ( m1_subset_1(c5_1__boolmark,c2_1__boolmark)
   => ( v1_funct_1(k1_funct_4(c3_1__boolmark,k2_funcop_1(c4_1__boolmark,c5_1__boolmark)))
      & v1_funct_2(k1_funct_4(c3_1__boolmark,k2_funcop_1(c4_1__boolmark,c5_1__boolmark)),c1_1__boolmark,c2_1__boolmark)
      & m2_relset_1(k1_funct_4(c3_1__boolmark,k2_funcop_1(c4_1__boolmark,c5_1__boolmark)),c1_1__boolmark,c2_1__boolmark) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c2_1__boolmark,dt_c3_1__boolmark,dt_c4_1__boolmark,dt_c1_1__boolmark]),discharge_asm(discharge,[dt_c5_1__boolmark])],[dt_c5_1__boolmark,i4_1__boolmark]),
    [interesting(0.8),i3_1__boolmark]).

fof(i3_1__boolmark,plain,(
    ! [A] : 
      ( m1_subset_1(A,c2_1__boolmark)
     => ( v1_funct_1(k1_funct_4(c3_1__boolmark,k2_funcop_1(c4_1__boolmark,A)))
        & v1_funct_2(k1_funct_4(c3_1__boolmark,k2_funcop_1(c4_1__boolmark,A)),c1_1__boolmark,c2_1__boolmark)
        & m2_relset_1(k1_funct_4(c3_1__boolmark,k2_funcop_1(c4_1__boolmark,A)),c1_1__boolmark,c2_1__boolmark) ) ) ),
    inference(let,[status(thm),assumptions([dt_c2_1__boolmark,dt_c3_1__boolmark,dt_c4_1__boolmark,dt_c1_1__boolmark])],[i4_1_tmp__boolmark,dh_c5_1__boolmark]),
    [interesting(0.8),file(boolmark,i3_1__boolmark),[file(boolmark,i3_1__boolmark)]]).

fof(i3_1_tmp__boolmark,plain,
    ( m1_subset_1(c4_1__boolmark,k1_zfmisc_1(c1_1__boolmark))
   => ! [A] : 
        ( m1_subset_1(A,c2_1__boolmark)
       => ( v1_funct_1(k1_funct_4(c3_1__boolmark,k2_funcop_1(c4_1__boolmark,A)))
          & v1_funct_2(k1_funct_4(c3_1__boolmark,k2_funcop_1(c4_1__boolmark,A)),c1_1__boolmark,c2_1__boolmark)
          & m2_relset_1(k1_funct_4(c3_1__boolmark,k2_funcop_1(c4_1__boolmark,A)),c1_1__boolmark,c2_1__boolmark) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c2_1__boolmark,dt_c3_1__boolmark,dt_c1_1__boolmark]),discharge_asm(discharge,[dt_c4_1__boolmark])],[dt_c4_1__boolmark,i3_1__boolmark]),
    [interesting(0.8),i2_1__boolmark]).

fof(i2_1__boolmark,plain,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(c1_1__boolmark))
     => ! [B] : 
          ( m1_subset_1(B,c2_1__boolmark)
         => ( v1_funct_1(k1_funct_4(c3_1__boolmark,k2_funcop_1(A,B)))
            & v1_funct_2(k1_funct_4(c3_1__boolmark,k2_funcop_1(A,B)),c1_1__boolmark,c2_1__boolmark)
            & m2_relset_1(k1_funct_4(c3_1__boolmark,k2_funcop_1(A,B)),c1_1__boolmark,c2_1__boolmark) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c2_1__boolmark,dt_c3_1__boolmark,dt_c1_1__boolmark])],[i3_1_tmp__boolmark,dh_c4_1__boolmark]),
    [interesting(0.8),file(boolmark,i2_1__boolmark),[file(boolmark,i2_1__boolmark)]]).

fof(i2_1_tmp__boolmark,plain,
    ( ( v1_funct_1(c3_1__boolmark)
      & v1_funct_2(c3_1__boolmark,c1_1__boolmark,c2_1__boolmark)
      & m2_relset_1(c3_1__boolmark,c1_1__boolmark,c2_1__boolmark) )
   => ! [A] : 
        ( m1_subset_1(A,k1_zfmisc_1(c1_1__boolmark))
       => ! [B] : 
            ( m1_subset_1(B,c2_1__boolmark)
           => ( v1_funct_1(k1_funct_4(c3_1__boolmark,k2_funcop_1(A,B)))
              & v1_funct_2(k1_funct_4(c3_1__boolmark,k2_funcop_1(A,B)),c1_1__boolmark,c2_1__boolmark)
              & m2_relset_1(k1_funct_4(c3_1__boolmark,k2_funcop_1(A,B)),c1_1__boolmark,c2_1__boolmark) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c2_1__boolmark,dt_c1_1__boolmark]),discharge_asm(discharge,[dt_c3_1__boolmark])],[dt_c3_1__boolmark,i2_1__boolmark]),
    [interesting(0.8),i1_1__boolmark]).

fof(i1_1__boolmark,plain,(
    ! [A] : 
      ( ( v1_funct_1(A)
        & v1_funct_2(A,c1_1__boolmark,c2_1__boolmark)
        & m2_relset_1(A,c1_1__boolmark,c2_1__boolmark) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(c1_1__boolmark))
         => ! [C] : 
              ( m1_subset_1(C,c2_1__boolmark)
             => ( v1_funct_1(k1_funct_4(A,k2_funcop_1(B,C)))
                & v1_funct_2(k1_funct_4(A,k2_funcop_1(B,C)),c1_1__boolmark,c2_1__boolmark)
                & m2_relset_1(k1_funct_4(A,k2_funcop_1(B,C)),c1_1__boolmark,c2_1__boolmark) ) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c2_1__boolmark,dt_c1_1__boolmark])],[i2_1_tmp__boolmark,dh_c3_1__boolmark]),
    [interesting(0.8),file(boolmark,i1_1__boolmark),[file(boolmark,i1_1__boolmark)]]).

fof(i1_1_tmp__boolmark,plain,
    ( ( ~ v1_xboole_0(c1_1__boolmark)
      & ~ v1_xboole_0(c2_1__boolmark) )
   => ! [A] : 
        ( ( v1_funct_1(A)
          & v1_funct_2(A,c1_1__boolmark,c2_1__boolmark)
          & m2_relset_1(A,c1_1__boolmark,c2_1__boolmark) )
       => ! [B] : 
            ( m1_subset_1(B,k1_zfmisc_1(c1_1__boolmark))
           => ! [C] : 
                ( m1_subset_1(C,c2_1__boolmark)
               => ( v1_funct_1(k1_funct_4(A,k2_funcop_1(B,C)))
                  & v1_funct_2(k1_funct_4(A,k2_funcop_1(B,C)),c1_1__boolmark,c2_1__boolmark)
                  & m2_relset_1(k1_funct_4(A,k2_funcop_1(B,C)),c1_1__boolmark,c2_1__boolmark) ) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_1__boolmark,dt_c2_1__boolmark])],[dt_c1_1__boolmark,dt_c2_1__boolmark,i1_1__boolmark]),
    [interesting(1),t1_boolmark]).

fof(t1_boolmark,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,B)
                & m2_relset_1(C,A,B) )
             => ! [D] : 
                  ( m1_subset_1(D,k1_zfmisc_1(A))
                 => ! [E] : 
                      ( m1_subset_1(E,B)
                     => ( v1_funct_1(k1_funct_4(C,k2_funcop_1(D,E)))
                        & v1_funct_2(k1_funct_4(C,k2_funcop_1(D,E)),A,B)
                        & m2_relset_1(k1_funct_4(C,k2_funcop_1(D,E)),A,B) ) ) ) ) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_1_tmp__boolmark,dh_c1_1__boolmark,dh_c2_1__boolmark]),
    [interesting(1),file(boolmark,t1_boolmark),[file(boolmark,t1_boolmark)]]).