% Mizar ND problem: t8_funct_2,funct_2,168,24 
fof(dh_c1_10__funct_2,definition,
    ( ! [A,B,C] : 
        ( ( v1_funct_1(C)
          & v1_funct_2(C,c1_10__funct_2,A)
          & m2_relset_1(C,c1_10__funct_2,A) )
       => ( r1_tarski(k2_relat_1(C),B)
         => ( ( A = k1_xboole_0
              & c1_10__funct_2 != k1_xboole_0 )
            | ( v1_funct_1(C)
              & v1_funct_2(C,c1_10__funct_2,B)
              & m2_relset_1(C,c1_10__funct_2,B) ) ) ) )
   => ! [D,E,F,G] : 
        ( ( v1_funct_1(G)
          & v1_funct_2(G,D,E)
          & m2_relset_1(G,D,E) )
       => ( r1_tarski(k2_relat_1(G),F)
         => ( ( E = k1_xboole_0
              & D != k1_xboole_0 )
            | ( v1_funct_1(G)
              & v1_funct_2(G,D,F)
              & m2_relset_1(G,D,F) ) ) ) ) ),
    introduced(definition,[new_symbol(c1_10__funct_2),file(funct_2,c1_10__funct_2)]),
    [interesting(0.8),axiom,file(funct_2,c1_10__funct_2)]).

fof(dh_c2_10__funct_2,definition,
    ( ! [A,B] : 
        ( ( v1_funct_1(B)
          & v1_funct_2(B,c1_10__funct_2,c2_10__funct_2)
          & m2_relset_1(B,c1_10__funct_2,c2_10__funct_2) )
       => ( r1_tarski(k2_relat_1(B),A)
         => ( ( c2_10__funct_2 = k1_xboole_0
              & c1_10__funct_2 != k1_xboole_0 )
            | ( v1_funct_1(B)
              & v1_funct_2(B,c1_10__funct_2,A)
              & m2_relset_1(B,c1_10__funct_2,A) ) ) ) )
   => ! [C,D,E] : 
        ( ( v1_funct_1(E)
          & v1_funct_2(E,c1_10__funct_2,C)
          & m2_relset_1(E,c1_10__funct_2,C) )
       => ( r1_tarski(k2_relat_1(E),D)
         => ( ( C = k1_xboole_0
              & c1_10__funct_2 != k1_xboole_0 )
            | ( v1_funct_1(E)
              & v1_funct_2(E,c1_10__funct_2,D)
              & m2_relset_1(E,c1_10__funct_2,D) ) ) ) ) ),
    introduced(definition,[new_symbol(c2_10__funct_2),file(funct_2,c2_10__funct_2)]),
    [interesting(0.8),axiom,file(funct_2,c2_10__funct_2)]).

fof(dh_c3_10__funct_2,definition,
    ( ! [A] : 
        ( ( v1_funct_1(A)
          & v1_funct_2(A,c1_10__funct_2,c2_10__funct_2)
          & m2_relset_1(A,c1_10__funct_2,c2_10__funct_2) )
       => ( r1_tarski(k2_relat_1(A),c3_10__funct_2)
         => ( ( c2_10__funct_2 = k1_xboole_0
              & c1_10__funct_2 != k1_xboole_0 )
            | ( v1_funct_1(A)
              & v1_funct_2(A,c1_10__funct_2,c3_10__funct_2)
              & m2_relset_1(A,c1_10__funct_2,c3_10__funct_2) ) ) ) )
   => ! [B,C] : 
        ( ( v1_funct_1(C)
          & v1_funct_2(C,c1_10__funct_2,c2_10__funct_2)
          & m2_relset_1(C,c1_10__funct_2,c2_10__funct_2) )
       => ( r1_tarski(k2_relat_1(C),B)
         => ( ( c2_10__funct_2 = k1_xboole_0
              & c1_10__funct_2 != k1_xboole_0 )
            | ( v1_funct_1(C)
              & v1_funct_2(C,c1_10__funct_2,B)
              & m2_relset_1(C,c1_10__funct_2,B) ) ) ) ) ),
    introduced(definition,[new_symbol(c3_10__funct_2),file(funct_2,c3_10__funct_2)]),
    [interesting(0.8),axiom,file(funct_2,c3_10__funct_2)]).

fof(dh_c4_10__funct_2,definition,
    ( ( ( v1_funct_1(c4_10__funct_2)
        & v1_funct_2(c4_10__funct_2,c1_10__funct_2,c2_10__funct_2)
        & m2_relset_1(c4_10__funct_2,c1_10__funct_2,c2_10__funct_2) )
     => ( r1_tarski(k2_relat_1(c4_10__funct_2),c3_10__funct_2)
       => ( ( c2_10__funct_2 = k1_xboole_0
            & c1_10__funct_2 != k1_xboole_0 )
          | ( v1_funct_1(c4_10__funct_2)
            & v1_funct_2(c4_10__funct_2,c1_10__funct_2,c3_10__funct_2)
            & m2_relset_1(c4_10__funct_2,c1_10__funct_2,c3_10__funct_2) ) ) ) )
   => ! [A] : 
        ( ( v1_funct_1(A)
          & v1_funct_2(A,c1_10__funct_2,c2_10__funct_2)
          & m2_relset_1(A,c1_10__funct_2,c2_10__funct_2) )
       => ( r1_tarski(k2_relat_1(A),c3_10__funct_2)
         => ( ( c2_10__funct_2 = k1_xboole_0
              & c1_10__funct_2 != k1_xboole_0 )
            | ( v1_funct_1(A)
              & v1_funct_2(A,c1_10__funct_2,c3_10__funct_2)
              & m2_relset_1(A,c1_10__funct_2,c3_10__funct_2) ) ) ) ) ),
    introduced(definition,[new_symbol(c4_10__funct_2),file(funct_2,c4_10__funct_2)]),
    [interesting(0.8),axiom,file(funct_2,c4_10__funct_2)]).

fof(e1_10__funct_2,assumption,(
    ~ ( c2_10__funct_2 = k1_xboole_0
      & c1_10__funct_2 != k1_xboole_0 ) ),
    introduced(assumption,[file(funct_2,e1_10__funct_2)]),
    [interesting(0.8),axiom,file(funct_2,e1_10__funct_2)]).

fof(e3_10__funct_2,assumption,(
    r1_tarski(k2_relat_1(c4_10__funct_2),c3_10__funct_2) ),
    introduced(assumption,[file(funct_2,e3_10__funct_2)]),
    [interesting(0.8),axiom,file(funct_2,e3_10__funct_2)]).

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(rc1_partfun1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_xboole_0(A) ) ),
    file(partfun1,rc1_partfun1),
    [interesting(0.9),axiom,file(partfun1,rc1_partfun1)]).

fof(rc3_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A) ) ),
    file(funct_1,rc3_funct_1),
    [interesting(0.9),axiom,file(funct_1,rc3_funct_1)]).

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_funct_1,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_funct_1(A) ) ),
    file(funct_1,cc1_funct_1),
    [interesting(0.9),axiom,file(funct_1,cc1_funct_1)]).

fof(cc1_relat_1,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_relat_1(A) ) ),
    file(relat_1,cc1_relat_1),
    [interesting(0.9),axiom,file(relat_1,cc1_relat_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(cc2_funct_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_xboole_0(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v2_funct_1(A) ) ) ),
    file(funct_1,cc2_funct_1),
    [interesting(0.9),axiom,file(funct_1,cc2_funct_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(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(fc5_relat_1,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_relat_1(A) )
     => ~ v1_xboole_0(k1_relat_1(A)) ) ),
    file(relat_1,fc5_relat_1),
    [interesting(0.9),axiom,file(relat_1,fc5_relat_1)]).

fof(fc6_relat_1,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_relat_1(A) )
     => ~ v1_xboole_0(k2_relat_1(A)) ) ),
    file(relat_1,fc6_relat_1),
    [interesting(0.9),axiom,file(relat_1,fc6_relat_1)]).

fof(fc7_relat_1,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_xboole_0(k1_relat_1(A))
        & v1_relat_1(k1_relat_1(A)) ) ) ),
    file(relat_1,fc7_relat_1),
    [interesting(0.9),axiom,file(relat_1,fc7_relat_1)]).

fof(fc8_relat_1,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_xboole_0(k2_relat_1(A))
        & v1_relat_1(k2_relat_1(A)) ) ) ),
    file(relat_1,fc8_relat_1),
    [interesting(0.9),axiom,file(relat_1,fc8_relat_1)]).

fof(rc1_funct_2,theorem,(
    ! [A,B] : 
    ? [C] : 
      ( m1_relset_1(C,A,B)
      & v1_relat_1(C)
      & v1_funct_1(C)
      & v1_funct_2(C,A,B) ) ),
    file(funct_2,rc1_funct_2),
    [interesting(0.9),axiom,file(funct_2,rc1_funct_2)]).

fof(rc1_relat_1,theorem,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A) ) ),
    file(relat_1,rc1_relat_1),
    [interesting(0.9),axiom,file(relat_1,rc1_relat_1)]).

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

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

fof(rc2_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_xboole_0(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc2_funct_1),
    [interesting(0.9),axiom,file(funct_1,rc2_funct_1)]).

fof(rc2_partfun1,theorem,(
    ! [A,B] : 
    ? [C] : 
      ( m1_relset_1(C,A,B)
      & v1_relat_1(C)
      & v1_funct_1(C) ) ),
    file(partfun1,rc2_partfun1),
    [interesting(0.9),axiom,file(partfun1,rc2_partfun1)]).

fof(rc2_relat_1,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A) ) ),
    file(relat_1,rc2_relat_1),
    [interesting(0.9),axiom,file(relat_1,rc2_relat_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(rc2_xboole_0,theorem,(
    ? [A] : ~ v1_xboole_0(A) ),
    file(xboole_0,rc2_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,rc2_xboole_0)]).

fof(rc3_relat_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v3_relat_1(A) ) ),
    file(relat_1,rc3_relat_1),
    [interesting(0.9),axiom,file(relat_1,rc3_relat_1)]).

fof(rc4_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v3_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc4_funct_1),
    [interesting(0.9),axiom,file(funct_1,rc4_funct_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(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_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_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_10__funct_2,assumption,(
    $true ),
    introduced(assumption,[file(funct_2,c1_10__funct_2)]),
    [interesting(0.8),axiom,file(funct_2,c1_10__funct_2)]).

fof(dt_c2_10__funct_2,assumption,(
    $true ),
    introduced(assumption,[file(funct_2,c2_10__funct_2)]),
    [interesting(0.8),axiom,file(funct_2,c2_10__funct_2)]).

fof(dt_c3_10__funct_2,assumption,(
    $true ),
    introduced(assumption,[file(funct_2,c3_10__funct_2)]),
    [interesting(0.8),axiom,file(funct_2,c3_10__funct_2)]).

fof(dt_c4_10__funct_2,assumption,
    ( v1_funct_1(c4_10__funct_2)
    & v1_funct_2(c4_10__funct_2,c1_10__funct_2,c2_10__funct_2)
    & m2_relset_1(c4_10__funct_2,c1_10__funct_2,c2_10__funct_2) ),
    introduced(assumption,[file(funct_2,c4_10__funct_2)]),
    [interesting(0.8),axiom,file(funct_2,c4_10__funct_2)]).

fof(fc12_relat_1,theorem,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0)
    & v3_relat_1(k1_xboole_0) ),
    file(relat_1,fc12_relat_1),
    [interesting(0.9),axiom,file(relat_1,fc12_relat_1)]).

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

fof(fc4_relat_1,theorem,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0) ),
    file(relat_1,fc4_relat_1),
    [interesting(0.9),axiom,file(relat_1,fc4_relat_1)]).

fof(rc1_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc1_funct_1),
    [interesting(0.9),axiom,file(funct_1,rc1_funct_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(e1_10_1__funct_2,assumption,(
    c3_10__funct_2 = k1_xboole_0 ),
    introduced(assumption,[file(funct_2,e1_10_1__funct_2)]),
    [interesting(0.65),axiom,file(funct_2,e1_10_1__funct_2)]).

fof(t3_xboole_1,theorem,(
    ! [A] : 
      ( r1_tarski(A,k1_xboole_0)
     => A = k1_xboole_0 ) ),
    file(xboole_1,t3_xboole_1),
    [interesting(0.9),axiom,file(xboole_1,t3_xboole_1)]).

fof(e2_10_1__funct_2,plain,(
    k2_relat_1(c4_10__funct_2) = k1_xboole_0 ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_10__funct_2,dt_c2_10__funct_2,dt_c3_10__funct_2,dt_c4_10__funct_2,e1_10_1__funct_2,e3_10__funct_2])],[antisymmetry_r2_hidden,existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc4_subset_1,rc1_funct_2,rc1_partfun1,rc2_partfun1,rc3_funct_1,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_c1_10__funct_2,dt_c2_10__funct_2,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc1_subset_1,fc6_relat_1,fc8_relat_1,rc1_funct_1,rc1_relat_1,rc1_subset_1,rc1_xboole_0,rc2_funct_1,rc2_relat_1,rc2_subset_1,rc2_xboole_0,rc3_relat_1,rc4_funct_1,t2_subset,t7_boole,t8_boole,reflexivity_r1_tarski,dt_k1_xboole_0,dt_k2_relat_1,dt_c3_10__funct_2,dt_c4_10__funct_2,fc12_relat_1,fc1_xboole_0,fc4_relat_1,t3_subset,t6_boole,e1_10_1__funct_2,e3_10__funct_2,t3_xboole_1]),
    [interesting(0.65),file(funct_2,e2_10_1__funct_2),[file(funct_2,e2_10_1__funct_2)]]).

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(e2_10__funct_2,plain,(
    k4_relset_1(c1_10__funct_2,c2_10__funct_2,c4_10__funct_2) = c1_10__funct_2 ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_10__funct_2,dt_c2_10__funct_2,dt_c4_10__funct_2,e1_10__funct_2])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,rc1_partfun1,rc3_funct_1,t1_subset,t4_subset,t5_subset,existence_m1_relset_1,existence_m1_subset_1,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_m1_relset_1,dt_m1_subset_1,cc1_funct_1,cc1_relat_1,cc1_relset_1,cc2_funct_1,fc1_subset_1,fc4_subset_1,fc5_relat_1,fc7_relat_1,rc1_funct_1,rc1_funct_2,rc1_relat_1,rc1_subset_1,rc1_xboole_0,rc2_funct_1,rc2_partfun1,rc2_relat_1,rc2_subset_1,rc2_xboole_0,rc3_relat_1,rc4_funct_1,t2_subset,t3_subset,t7_boole,t8_boole,existence_m2_relset_1,redefinition_k4_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_k4_relset_1,dt_m2_relset_1,dt_c1_10__funct_2,dt_c2_10__funct_2,dt_c4_10__funct_2,fc12_relat_1,fc1_xboole_0,fc4_relat_1,t6_boole,e1_10__funct_2,d1_funct_2]),
    [interesting(0.8),file(funct_2,e2_10__funct_2),[file(funct_2,e2_10__funct_2)]]).

fof(t65_relat_1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( k1_relat_1(A) = k1_xboole_0
      <=> k2_relat_1(A) = k1_xboole_0 ) ) ),
    file(relat_1,t65_relat_1),
    [interesting(0.9),axiom,file(relat_1,t65_relat_1)]).

fof(e3_10_1__funct_2,plain,(
    c1_10__funct_2 = k1_xboole_0 ),
    inference(mizar_by,[status(thm),assumptions([dt_c3_10__funct_2,e1_10_1__funct_2,e3_10__funct_2,dt_c1_10__funct_2,dt_c2_10__funct_2,dt_c4_10__funct_2,e1_10__funct_2])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k2_zfmisc_1,cc1_relset_1,fc4_subset_1,rc1_partfun1,rc3_funct_1,t1_subset,t4_subset,t5_subset,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_zfmisc_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc1_subset_1,fc5_relat_1,fc6_relat_1,fc7_relat_1,fc8_relat_1,rc1_funct_1,rc1_funct_2,rc1_relat_1,rc1_subset_1,rc1_xboole_0,rc2_funct_1,rc2_partfun1,rc2_relat_1,rc2_subset_1,rc2_xboole_0,rc3_relat_1,rc4_funct_1,t2_subset,t3_subset,t7_boole,t8_boole,redefinition_k4_relset_1,dt_k1_relat_1,dt_k1_xboole_0,dt_k2_relat_1,dt_k4_relset_1,dt_c1_10__funct_2,dt_c2_10__funct_2,dt_c4_10__funct_2,fc12_relat_1,fc1_xboole_0,fc4_relat_1,t6_boole,e2_10_1__funct_2,e2_10__funct_2,t65_relat_1]),
    [interesting(0.65),file(funct_2,e3_10_1__funct_2),[file(funct_2,e3_10_1__funct_2)]]).

fof(i2_10_1__funct_2,theorem,(
    $true ),
    introduced(tautology,[file(funct_2,i2_10_1__funct_2)]),
    [interesting(0.65),trivial,file(funct_2,i2_10_1__funct_2)]).

fof(i1_10_1__funct_2,plain,(
    c1_10__funct_2 = k1_xboole_0 ),
    inference(conclusion,[status(thm),assumptions([dt_c3_10__funct_2,e1_10_1__funct_2,e3_10__funct_2,dt_c1_10__funct_2,dt_c2_10__funct_2,dt_c4_10__funct_2,e1_10__funct_2])],[e3_10_1__funct_2,i2_10_1__funct_2]),
    [interesting(0.65),file(funct_2,i1_10_1__funct_2),[file(funct_2,i1_10_1__funct_2)]]).

fof(e4_10__funct_2,plain,
    ( c3_10__funct_2 = k1_xboole_0
   => c1_10__funct_2 = k1_xboole_0 ),
    inference(discharge_asm,[status(thm),assumptions([dt_c3_10__funct_2,e3_10__funct_2,dt_c1_10__funct_2,dt_c2_10__funct_2,dt_c4_10__funct_2,e1_10__funct_2]),discharge_asm(discharge,[e1_10_1__funct_2])],[e1_10_1__funct_2,i1_10_1__funct_2]),
    [interesting(0.8),file(funct_2,e4_10__funct_2),[file(funct_2,e4_10__funct_2)]]).

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(e5_10__funct_2,plain,
    ( v1_funct_1(c4_10__funct_2)
    & v1_funct_2(c4_10__funct_2,c1_10__funct_2,c3_10__funct_2)
    & m2_relset_1(c4_10__funct_2,c1_10__funct_2,c3_10__funct_2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c3_10__funct_2,dt_c1_10__funct_2,dt_c2_10__funct_2,dt_c4_10__funct_2,e1_10__funct_2,e3_10__funct_2])],[antisymmetry_r2_hidden,rc1_partfun1,rc3_funct_1,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_funct_1,cc1_relat_1,cc1_relset_1,cc2_funct_1,fc1_subset_1,fc4_subset_1,fc5_relat_1,fc6_relat_1,fc7_relat_1,fc8_relat_1,rc1_funct_2,rc1_relat_1,rc1_subset_1,rc1_xboole_0,rc2_funct_1,rc2_partfun1,rc2_relat_1,rc2_subset_1,rc2_xboole_0,rc3_relat_1,rc4_funct_1,t2_subset,t7_boole,t8_boole,reflexivity_r1_tarski,existence_m2_relset_1,redefinition_k4_relset_1,redefinition_m2_relset_1,dt_k1_relat_1,dt_k1_xboole_0,dt_k2_relat_1,dt_k4_relset_1,dt_m2_relset_1,dt_c1_10__funct_2,dt_c2_10__funct_2,dt_c3_10__funct_2,dt_c4_10__funct_2,fc12_relat_1,fc1_xboole_0,fc4_relat_1,rc1_funct_1,t3_subset,t6_boole,e4_10__funct_2,e2_10__funct_2,e3_10__funct_2,d1_funct_2,t11_relset_1]),
    [interesting(0.8),file(funct_2,e5_10__funct_2),[file(funct_2,e5_10__funct_2)]]).

fof(i7_10__funct_2,theorem,(
    $true ),
    introduced(tautology,[file(funct_2,i7_10__funct_2)]),
    [interesting(0.8),trivial,file(funct_2,i7_10__funct_2)]).

fof(i6_10__funct_2,plain,
    ( v1_funct_1(c4_10__funct_2)
    & v1_funct_2(c4_10__funct_2,c1_10__funct_2,c3_10__funct_2)
    & m2_relset_1(c4_10__funct_2,c1_10__funct_2,c3_10__funct_2) ),
    inference(conclusion,[status(thm),assumptions([dt_c3_10__funct_2,dt_c1_10__funct_2,dt_c2_10__funct_2,dt_c4_10__funct_2,e1_10__funct_2,e3_10__funct_2])],[e5_10__funct_2,i7_10__funct_2]),
    [interesting(0.8),file(funct_2,i6_10__funct_2),[file(funct_2,i6_10__funct_2)]]).

fof(i5_10__funct_2,plain,(
    ~ ( r1_tarski(k2_relat_1(c4_10__funct_2),c3_10__funct_2)
      & ~ ( v1_funct_1(c4_10__funct_2)
          & v1_funct_2(c4_10__funct_2,c1_10__funct_2,c3_10__funct_2)
          & m2_relset_1(c4_10__funct_2,c1_10__funct_2,c3_10__funct_2) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c3_10__funct_2,dt_c1_10__funct_2,dt_c2_10__funct_2,dt_c4_10__funct_2,e1_10__funct_2]),discharge_asm(discharge,[e3_10__funct_2])],[e3_10__funct_2,i6_10__funct_2]),
    [interesting(0.8),file(funct_2,i5_10__funct_2),[file(funct_2,i5_10__funct_2)]]).

fof(i4_10__funct_2,plain,
    ( r1_tarski(k2_relat_1(c4_10__funct_2),c3_10__funct_2)
   => ( ( c2_10__funct_2 = k1_xboole_0
        & c1_10__funct_2 != k1_xboole_0 )
      | ( v1_funct_1(c4_10__funct_2)
        & v1_funct_2(c4_10__funct_2,c1_10__funct_2,c3_10__funct_2)
        & m2_relset_1(c4_10__funct_2,c1_10__funct_2,c3_10__funct_2) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c3_10__funct_2,dt_c1_10__funct_2,dt_c2_10__funct_2,dt_c4_10__funct_2]),discharge_asm(discharge,[e1_10__funct_2])],[e1_10__funct_2,i5_10__funct_2]),
    [interesting(0.8),file(funct_2,i4_10__funct_2),[file(funct_2,i4_10__funct_2)]]).

fof(i4_10_tmp__funct_2,plain,
    ( ( v1_funct_1(c4_10__funct_2)
      & v1_funct_2(c4_10__funct_2,c1_10__funct_2,c2_10__funct_2)
      & m2_relset_1(c4_10__funct_2,c1_10__funct_2,c2_10__funct_2) )
   => ( r1_tarski(k2_relat_1(c4_10__funct_2),c3_10__funct_2)
     => ( ( c2_10__funct_2 = k1_xboole_0
          & c1_10__funct_2 != k1_xboole_0 )
        | ( v1_funct_1(c4_10__funct_2)
          & v1_funct_2(c4_10__funct_2,c1_10__funct_2,c3_10__funct_2)
          & m2_relset_1(c4_10__funct_2,c1_10__funct_2,c3_10__funct_2) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c3_10__funct_2,dt_c1_10__funct_2,dt_c2_10__funct_2]),discharge_asm(discharge,[dt_c4_10__funct_2])],[dt_c4_10__funct_2,i4_10__funct_2]),
    [interesting(0.8),i3_10__funct_2]).

fof(i3_10__funct_2,plain,(
    ! [A] : 
      ( ( v1_funct_1(A)
        & v1_funct_2(A,c1_10__funct_2,c2_10__funct_2)
        & m2_relset_1(A,c1_10__funct_2,c2_10__funct_2) )
     => ( r1_tarski(k2_relat_1(A),c3_10__funct_2)
       => ( ( c2_10__funct_2 = k1_xboole_0
            & c1_10__funct_2 != k1_xboole_0 )
          | ( v1_funct_1(A)
            & v1_funct_2(A,c1_10__funct_2,c3_10__funct_2)
            & m2_relset_1(A,c1_10__funct_2,c3_10__funct_2) ) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c3_10__funct_2,dt_c1_10__funct_2,dt_c2_10__funct_2])],[i4_10_tmp__funct_2,dh_c4_10__funct_2]),
    [interesting(0.8),file(funct_2,i3_10__funct_2),[file(funct_2,i3_10__funct_2)]]).

fof(i3_10_tmp__funct_2,plain,(
    ! [A] : 
      ( ( v1_funct_1(A)
        & v1_funct_2(A,c1_10__funct_2,c2_10__funct_2)
        & m2_relset_1(A,c1_10__funct_2,c2_10__funct_2) )
     => ( r1_tarski(k2_relat_1(A),c3_10__funct_2)
       => ( ( c2_10__funct_2 = k1_xboole_0
            & c1_10__funct_2 != k1_xboole_0 )
          | ( v1_funct_1(A)
            & v1_funct_2(A,c1_10__funct_2,c3_10__funct_2)
            & m2_relset_1(A,c1_10__funct_2,c3_10__funct_2) ) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_10__funct_2,dt_c2_10__funct_2]),discharge_asm(discharge,[dt_c3_10__funct_2])],[dt_c3_10__funct_2,i3_10__funct_2]),
    [interesting(0.8),i2_10__funct_2]).

fof(i2_10__funct_2,plain,(
    ! [A,B] : 
      ( ( v1_funct_1(B)
        & v1_funct_2(B,c1_10__funct_2,c2_10__funct_2)
        & m2_relset_1(B,c1_10__funct_2,c2_10__funct_2) )
     => ( r1_tarski(k2_relat_1(B),A)
       => ( ( c2_10__funct_2 = k1_xboole_0
            & c1_10__funct_2 != k1_xboole_0 )
          | ( v1_funct_1(B)
            & v1_funct_2(B,c1_10__funct_2,A)
            & m2_relset_1(B,c1_10__funct_2,A) ) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_10__funct_2,dt_c2_10__funct_2])],[i3_10_tmp__funct_2,dh_c3_10__funct_2]),
    [interesting(0.8),file(funct_2,i2_10__funct_2),[file(funct_2,i2_10__funct_2)]]).

fof(i2_10_tmp__funct_2,plain,(
    ! [A,B] : 
      ( ( v1_funct_1(B)
        & v1_funct_2(B,c1_10__funct_2,c2_10__funct_2)
        & m2_relset_1(B,c1_10__funct_2,c2_10__funct_2) )
     => ( r1_tarski(k2_relat_1(B),A)
       => ( ( c2_10__funct_2 = k1_xboole_0
            & c1_10__funct_2 != k1_xboole_0 )
          | ( v1_funct_1(B)
            & v1_funct_2(B,c1_10__funct_2,A)
            & m2_relset_1(B,c1_10__funct_2,A) ) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_10__funct_2]),discharge_asm(discharge,[dt_c2_10__funct_2])],[dt_c2_10__funct_2,i2_10__funct_2]),
    [interesting(0.8),i1_10__funct_2]).

fof(i1_10__funct_2,plain,(
    ! [A,B,C] : 
      ( ( v1_funct_1(C)
        & v1_funct_2(C,c1_10__funct_2,A)
        & m2_relset_1(C,c1_10__funct_2,A) )
     => ( r1_tarski(k2_relat_1(C),B)
       => ( ( A = k1_xboole_0
            & c1_10__funct_2 != k1_xboole_0 )
          | ( v1_funct_1(C)
            & v1_funct_2(C,c1_10__funct_2,B)
            & m2_relset_1(C,c1_10__funct_2,B) ) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_10__funct_2])],[i2_10_tmp__funct_2,dh_c2_10__funct_2]),
    [interesting(0.8),file(funct_2,i1_10__funct_2),[file(funct_2,i1_10__funct_2)]]).

fof(i1_10_tmp__funct_2,plain,(
    ! [A,B,C] : 
      ( ( v1_funct_1(C)
        & v1_funct_2(C,c1_10__funct_2,A)
        & m2_relset_1(C,c1_10__funct_2,A) )
     => ( r1_tarski(k2_relat_1(C),B)
       => ( ( A = k1_xboole_0
            & c1_10__funct_2 != k1_xboole_0 )
          | ( v1_funct_1(C)
            & v1_funct_2(C,c1_10__funct_2,B)
            & m2_relset_1(C,c1_10__funct_2,B) ) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_10__funct_2])],[dt_c1_10__funct_2,i1_10__funct_2]),
    [interesting(1),t8_funct_2]).

fof(t8_funct_2,theorem,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m2_relset_1(D,A,B) )
     => ( r1_tarski(k2_relat_1(D),C)
       => ( ( B = k1_xboole_0
            & A != k1_xboole_0 )
          | ( v1_funct_1(D)
            & v1_funct_2(D,A,C)
            & m2_relset_1(D,A,C) ) ) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_10_tmp__funct_2,dh_c1_10__funct_2]),
    [interesting(1),file(funct_2,t8_funct_2),[file(funct_2,t8_funct_2)]]).