% Mizar ND problem: t19_funct_6,funct_6,416,61 
fof(dh_c1_19__funct_6,definition,
    ( ! [A,B,C] : 
        ( ( v1_relat_1(C)
          & v1_funct_1(C) )
       => ( r2_hidden(C,k1_funct_2(k2_zfmisc_1(c1_19__funct_6,A),B))
         => ( k2_zfmisc_1(c1_19__funct_6,A) = k1_xboole_0
            | ( r2_hidden(k3_funct_5(C),k1_funct_2(c1_19__funct_6,k1_funct_2(A,B)))
              & r2_hidden(k5_funct_5(C),k1_funct_2(A,k1_funct_2(c1_19__funct_6,B))) ) ) ) )
   => ! [D,E,F,G] : 
        ( ( v1_relat_1(G)
          & v1_funct_1(G) )
       => ( r2_hidden(G,k1_funct_2(k2_zfmisc_1(D,E),F))
         => ( k2_zfmisc_1(D,E) = k1_xboole_0
            | ( r2_hidden(k3_funct_5(G),k1_funct_2(D,k1_funct_2(E,F)))
              & r2_hidden(k5_funct_5(G),k1_funct_2(E,k1_funct_2(D,F))) ) ) ) ) ),
    introduced(definition,[new_symbol(c1_19__funct_6),file(funct_6,c1_19__funct_6)]),
    [interesting(0.8),axiom,file(funct_6,c1_19__funct_6)]).

fof(dh_c2_19__funct_6,definition,
    ( ! [A,B] : 
        ( ( v1_relat_1(B)
          & v1_funct_1(B) )
       => ( r2_hidden(B,k1_funct_2(k2_zfmisc_1(c1_19__funct_6,c2_19__funct_6),A))
         => ( k2_zfmisc_1(c1_19__funct_6,c2_19__funct_6) = k1_xboole_0
            | ( r2_hidden(k3_funct_5(B),k1_funct_2(c1_19__funct_6,k1_funct_2(c2_19__funct_6,A)))
              & r2_hidden(k5_funct_5(B),k1_funct_2(c2_19__funct_6,k1_funct_2(c1_19__funct_6,A))) ) ) ) )
   => ! [C,D,E] : 
        ( ( v1_relat_1(E)
          & v1_funct_1(E) )
       => ( r2_hidden(E,k1_funct_2(k2_zfmisc_1(c1_19__funct_6,C),D))
         => ( k2_zfmisc_1(c1_19__funct_6,C) = k1_xboole_0
            | ( r2_hidden(k3_funct_5(E),k1_funct_2(c1_19__funct_6,k1_funct_2(C,D)))
              & r2_hidden(k5_funct_5(E),k1_funct_2(C,k1_funct_2(c1_19__funct_6,D))) ) ) ) ) ),
    introduced(definition,[new_symbol(c2_19__funct_6),file(funct_6,c2_19__funct_6)]),
    [interesting(0.8),axiom,file(funct_6,c2_19__funct_6)]).

fof(dh_c3_19__funct_6,definition,
    ( ! [A] : 
        ( ( v1_relat_1(A)
          & v1_funct_1(A) )
       => ( r2_hidden(A,k1_funct_2(k2_zfmisc_1(c1_19__funct_6,c2_19__funct_6),c3_19__funct_6))
         => ( k2_zfmisc_1(c1_19__funct_6,c2_19__funct_6) = k1_xboole_0
            | ( r2_hidden(k3_funct_5(A),k1_funct_2(c1_19__funct_6,k1_funct_2(c2_19__funct_6,c3_19__funct_6)))
              & r2_hidden(k5_funct_5(A),k1_funct_2(c2_19__funct_6,k1_funct_2(c1_19__funct_6,c3_19__funct_6))) ) ) ) )
   => ! [B,C] : 
        ( ( v1_relat_1(C)
          & v1_funct_1(C) )
       => ( r2_hidden(C,k1_funct_2(k2_zfmisc_1(c1_19__funct_6,c2_19__funct_6),B))
         => ( k2_zfmisc_1(c1_19__funct_6,c2_19__funct_6) = k1_xboole_0
            | ( r2_hidden(k3_funct_5(C),k1_funct_2(c1_19__funct_6,k1_funct_2(c2_19__funct_6,B)))
              & r2_hidden(k5_funct_5(C),k1_funct_2(c2_19__funct_6,k1_funct_2(c1_19__funct_6,B))) ) ) ) ) ),
    introduced(definition,[new_symbol(c3_19__funct_6),file(funct_6,c3_19__funct_6)]),
    [interesting(0.8),axiom,file(funct_6,c3_19__funct_6)]).

fof(dh_c4_19__funct_6,definition,
    ( ( ( v1_relat_1(c4_19__funct_6)
        & v1_funct_1(c4_19__funct_6) )
     => ( r2_hidden(c4_19__funct_6,k1_funct_2(k2_zfmisc_1(c1_19__funct_6,c2_19__funct_6),c3_19__funct_6))
       => ( k2_zfmisc_1(c1_19__funct_6,c2_19__funct_6) = k1_xboole_0
          | ( r2_hidden(k3_funct_5(c4_19__funct_6),k1_funct_2(c1_19__funct_6,k1_funct_2(c2_19__funct_6,c3_19__funct_6)))
            & r2_hidden(k5_funct_5(c4_19__funct_6),k1_funct_2(c2_19__funct_6,k1_funct_2(c1_19__funct_6,c3_19__funct_6))) ) ) ) )
   => ! [A] : 
        ( ( v1_relat_1(A)
          & v1_funct_1(A) )
       => ( r2_hidden(A,k1_funct_2(k2_zfmisc_1(c1_19__funct_6,c2_19__funct_6),c3_19__funct_6))
         => ( k2_zfmisc_1(c1_19__funct_6,c2_19__funct_6) = k1_xboole_0
            | ( r2_hidden(k3_funct_5(A),k1_funct_2(c1_19__funct_6,k1_funct_2(c2_19__funct_6,c3_19__funct_6)))
              & r2_hidden(k5_funct_5(A),k1_funct_2(c2_19__funct_6,k1_funct_2(c1_19__funct_6,c3_19__funct_6))) ) ) ) ) ),
    introduced(definition,[new_symbol(c4_19__funct_6),file(funct_6,c4_19__funct_6)]),
    [interesting(0.8),axiom,file(funct_6,c4_19__funct_6)]).

fof(e1_19__funct_6,assumption,(
    k2_zfmisc_1(c1_19__funct_6,c2_19__funct_6) != k1_xboole_0 ),
    introduced(assumption,[file(funct_6,e1_19__funct_6)]),
    [interesting(0.8),axiom,file(funct_6,e1_19__funct_6)]).

fof(e2_19__funct_6,assumption,(
    r2_hidden(c4_19__funct_6,k1_funct_2(k2_zfmisc_1(c1_19__funct_6,c2_19__funct_6),c3_19__funct_6)) ),
    introduced(assumption,[file(funct_6,e2_19__funct_6)]),
    [interesting(0.8),axiom,file(funct_6,e2_19__funct_6)]).

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

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(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(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(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(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_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(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_funct_2,theorem,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => ~ v1_xboole_0(k1_funct_2(A,B)) ) ),
    file(funct_2,fc1_funct_2),
    [interesting(0.9),axiom,file(funct_2,fc1_funct_2)]).

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(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_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(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_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(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(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(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(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(antisymmetry_r2_hidden,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => ~ r2_hidden(B,A) ) ),
    file(hidden,r2_hidden),
    [interesting(0.9),axiom,file(hidden,r2_hidden)]).

fof(dt_k1_funct_2,axiom,(
    $true ),
    file(funct_2,k1_funct_2),
    [interesting(0.9),axiom,file(funct_2,k1_funct_2)]).

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

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

fof(dt_k3_funct_5,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(k3_funct_5(A))
        & v1_funct_1(k3_funct_5(A)) ) ) ),
    file(funct_5,k3_funct_5),
    [interesting(0.9),axiom,file(funct_5,k3_funct_5)]).

fof(dt_k5_funct_5,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(k5_funct_5(A))
        & v1_funct_1(k5_funct_5(A)) ) ) ),
    file(funct_5,k5_funct_5),
    [interesting(0.9),axiom,file(funct_5,k5_funct_5)]).

fof(dt_c1_19__funct_6,assumption,(
    $true ),
    introduced(assumption,[file(funct_6,c1_19__funct_6)]),
    [interesting(0.8),axiom,file(funct_6,c1_19__funct_6)]).

fof(dt_c2_19__funct_6,assumption,(
    $true ),
    introduced(assumption,[file(funct_6,c2_19__funct_6)]),
    [interesting(0.8),axiom,file(funct_6,c2_19__funct_6)]).

fof(dt_c3_19__funct_6,assumption,(
    $true ),
    introduced(assumption,[file(funct_6,c3_19__funct_6)]),
    [interesting(0.8),axiom,file(funct_6,c3_19__funct_6)]).

fof(dt_c4_19__funct_6,assumption,
    ( v1_relat_1(c4_19__funct_6)
    & v1_funct_1(c4_19__funct_6) ),
    introduced(assumption,[file(funct_6,c4_19__funct_6)]),
    [interesting(0.8),axiom,file(funct_6,c4_19__funct_6)]).

fof(fc2_funct_2,theorem,(
    ! [A] : ~ v1_xboole_0(k1_funct_2(A,A)) ),
    file(funct_2,fc2_funct_2),
    [interesting(0.9),axiom,file(funct_2,fc2_funct_2)]).

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

fof(d2_funct_2,definition,(
    ! [A,B,C] : 
      ( C = k1_funct_2(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ? [E] : 
              ( v1_relat_1(E)
              & v1_funct_1(E)
              & D = E
              & k1_relat_1(E) = A
              & r1_tarski(k2_relat_1(E),B) ) ) ) ),
    file(funct_2,d2_funct_2),
    [interesting(0.9),axiom,file(funct_2,d2_funct_2)]).

fof(e3_19__funct_6,plain,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & c4_19__funct_6 = A
      & k1_relat_1(A) = k2_zfmisc_1(c1_19__funct_6,c2_19__funct_6)
      & r1_tarski(k2_relat_1(A),c3_19__funct_6) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_19__funct_6,dt_c2_19__funct_6,dt_c3_19__funct_6,dt_c4_19__funct_6,e2_19__funct_6])],[cc1_finseq_1,fc11_finseq_1,fc17_finseq_1,rc1_finseq_1,rc3_finseq_1,rc3_relat_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,dt_k1_xboole_0,fc12_relat_1,fc2_finseq_1,fc4_relat_1,rc3_funct_1,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,cc1_funct_1,cc1_relat_1,cc1_relset_1,cc2_funct_1,fc1_funct_2,fc1_subset_1,fc4_subset_1,fc5_relat_1,fc6_relat_1,fc7_relat_1,fc8_relat_1,rc1_relat_1,rc1_subset_1,rc2_funct_1,rc2_relat_1,rc2_subset_1,t2_subset,t4_subset,t5_subset,t6_boole,t8_boole,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_funct_2,dt_k1_relat_1,dt_k2_relat_1,dt_k2_zfmisc_1,dt_c1_19__funct_6,dt_c2_19__funct_6,dt_c3_19__funct_6,dt_c4_19__funct_6,fc2_funct_2,rc1_funct_1,t1_subset,t3_subset,t7_boole,e2_19__funct_6,d2_funct_2]),
    [interesting(0.8),file(funct_6,e3_19__funct_6),[file(funct_6,e3_19__funct_6)]]).

fof(t42_funct_5,theorem,(
    ! [A,B,C] : 
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ( k1_relat_1(C) = k2_zfmisc_1(A,B)
       => ( r1_tarski(k2_relat_1(k3_funct_5(C)),k1_funct_2(B,k2_relat_1(C)))
          & r1_tarski(k2_relat_1(k5_funct_5(C)),k1_funct_2(A,k2_relat_1(C))) ) ) ) ),
    file(funct_5,t42_funct_5),
    [interesting(0.9),axiom,file(funct_5,t42_funct_5)]).

fof(t63_funct_5,theorem,(
    ! [A,B,C] : 
      ( r1_tarski(A,B)
     => r1_tarski(k1_funct_2(C,A),k1_funct_2(C,B)) ) ),
    file(funct_5,t63_funct_5),
    [interesting(0.9),axiom,file(funct_5,t63_funct_5)]).

fof(e4_19__funct_6,plain,
    ( r1_tarski(k2_relat_1(k3_funct_5(c4_19__funct_6)),k1_funct_2(c2_19__funct_6,k2_relat_1(c4_19__funct_6)))
    & r1_tarski(k2_relat_1(k5_funct_5(c4_19__funct_6)),k1_funct_2(c1_19__funct_6,k2_relat_1(c4_19__funct_6)))
    & r1_tarski(k1_funct_2(c2_19__funct_6,k2_relat_1(c4_19__funct_6)),k1_funct_2(c2_19__funct_6,c3_19__funct_6))
    & r1_tarski(k1_funct_2(c1_19__funct_6,k2_relat_1(c4_19__funct_6)),k1_funct_2(c1_19__funct_6,c3_19__funct_6)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_19__funct_6,dt_c2_19__funct_6,dt_c3_19__funct_6,dt_c4_19__funct_6,e2_19__funct_6])],[cc1_finseq_1,fc11_finseq_1,fc17_finseq_1,rc1_finseq_1,rc3_finseq_1,rc3_relat_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,antisymmetry_r2_hidden,dt_k1_xboole_0,fc12_relat_1,fc2_finseq_1,fc4_relat_1,rc3_funct_1,t1_subset,t4_subset,t5_subset,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,cc1_funct_1,cc1_relat_1,cc1_relset_1,cc2_funct_1,fc1_funct_2,fc1_subset_1,fc4_subset_1,fc5_relat_1,fc6_relat_1,fc7_relat_1,fc8_relat_1,rc1_relat_1,rc1_subset_1,rc2_funct_1,rc2_relat_1,rc2_subset_1,t2_subset,t6_boole,t7_boole,t8_boole,reflexivity_r1_tarski,dt_k1_funct_2,dt_k1_relat_1,dt_k2_relat_1,dt_k2_zfmisc_1,dt_k3_funct_5,dt_k5_funct_5,dt_c1_19__funct_6,dt_c2_19__funct_6,dt_c3_19__funct_6,dt_c4_19__funct_6,fc2_funct_2,rc1_funct_1,t3_subset,e3_19__funct_6,t42_funct_5,t63_funct_5]),
    [interesting(0.8),file(funct_6,e4_19__funct_6),[file(funct_6,e4_19__funct_6)]]).

fof(t31_funct_5,theorem,(
    ! [A,B,C] : 
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ( k1_relat_1(C) = k2_zfmisc_1(A,B)
       => ( k2_zfmisc_1(A,B) = k1_xboole_0
          | ( k1_relat_1(k3_funct_5(C)) = A
            & k1_relat_1(k5_funct_5(C)) = B ) ) ) ) ),
    file(funct_5,t31_funct_5),
    [interesting(0.9),axiom,file(funct_5,t31_funct_5)]).

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(e5_19__funct_6,plain,
    ( r1_tarski(k2_relat_1(k3_funct_5(c4_19__funct_6)),k1_funct_2(c2_19__funct_6,c3_19__funct_6))
    & r1_tarski(k2_relat_1(k5_funct_5(c4_19__funct_6)),k1_funct_2(c1_19__funct_6,c3_19__funct_6))
    & k1_relat_1(k3_funct_5(c4_19__funct_6)) = c1_19__funct_6
    & k1_relat_1(k5_funct_5(c4_19__funct_6)) = c2_19__funct_6 ),
    inference(mizar_by,[status(thm),assumptions([e1_19__funct_6,dt_c1_19__funct_6,dt_c2_19__funct_6,dt_c3_19__funct_6,dt_c4_19__funct_6,e2_19__funct_6])],[antisymmetry_r2_hidden,t1_subset,t4_subset,t5_subset,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,cc1_finseq_1,cc1_funct_1,cc1_relat_1,cc1_relset_1,cc2_funct_1,fc11_finseq_1,fc17_finseq_1,fc1_funct_2,fc1_subset_1,fc4_subset_1,fc5_relat_1,fc6_relat_1,fc7_relat_1,fc8_relat_1,rc1_finseq_1,rc1_relat_1,rc1_subset_1,rc2_funct_1,rc2_relat_1,rc2_subset_1,rc3_finseq_1,rc3_funct_1,rc3_relat_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t7_boole,t8_boole,reflexivity_r1_tarski,dt_k1_funct_2,dt_k1_relat_1,dt_k1_xboole_0,dt_k2_relat_1,dt_k2_zfmisc_1,dt_k3_funct_5,dt_k5_funct_5,dt_c1_19__funct_6,dt_c2_19__funct_6,dt_c3_19__funct_6,dt_c4_19__funct_6,fc12_relat_1,fc2_finseq_1,fc2_funct_2,fc4_relat_1,rc1_funct_1,t3_subset,t6_boole,e4_19__funct_6,e1_19__funct_6,e3_19__funct_6,t31_funct_5,t1_xboole_1]),
    [interesting(0.8),file(funct_6,e5_19__funct_6),[file(funct_6,e5_19__funct_6)]]).

fof(e6_19__funct_6,plain,
    ( r2_hidden(k3_funct_5(c4_19__funct_6),k1_funct_2(c1_19__funct_6,k1_funct_2(c2_19__funct_6,c3_19__funct_6)))
    & r2_hidden(k5_funct_5(c4_19__funct_6),k1_funct_2(c2_19__funct_6,k1_funct_2(c1_19__funct_6,c3_19__funct_6))) ),
    inference(mizar_by,[status(thm),assumptions([e1_19__funct_6,dt_c1_19__funct_6,dt_c2_19__funct_6,dt_c3_19__funct_6,dt_c4_19__funct_6,e2_19__funct_6])],[cc1_finseq_1,fc11_finseq_1,fc17_finseq_1,rc1_finseq_1,rc3_finseq_1,rc3_relat_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,dt_k1_xboole_0,fc12_relat_1,fc2_finseq_1,fc4_relat_1,rc3_funct_1,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc1_funct_2,fc1_subset_1,fc5_relat_1,fc6_relat_1,fc7_relat_1,fc8_relat_1,rc1_relat_1,rc1_subset_1,rc2_funct_1,rc2_relat_1,rc2_subset_1,t2_subset,t4_subset,t5_subset,t6_boole,t8_boole,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_funct_2,dt_k1_relat_1,dt_k2_relat_1,dt_k3_funct_5,dt_k5_funct_5,dt_c1_19__funct_6,dt_c2_19__funct_6,dt_c3_19__funct_6,dt_c4_19__funct_6,fc2_funct_2,rc1_funct_1,t1_subset,t3_subset,t7_boole,e5_19__funct_6,d2_funct_2]),
    [interesting(0.8),file(funct_6,e6_19__funct_6),[file(funct_6,e6_19__funct_6)]]).

fof(i7_19__funct_6,theorem,(
    $true ),
    introduced(tautology,[file(funct_6,i7_19__funct_6)]),
    [interesting(0.8),trivial,file(funct_6,i7_19__funct_6)]).

fof(i6_19__funct_6,plain,
    ( r2_hidden(k3_funct_5(c4_19__funct_6),k1_funct_2(c1_19__funct_6,k1_funct_2(c2_19__funct_6,c3_19__funct_6)))
    & r2_hidden(k5_funct_5(c4_19__funct_6),k1_funct_2(c2_19__funct_6,k1_funct_2(c1_19__funct_6,c3_19__funct_6))) ),
    inference(conclusion,[status(thm),assumptions([e1_19__funct_6,dt_c1_19__funct_6,dt_c2_19__funct_6,dt_c3_19__funct_6,dt_c4_19__funct_6,e2_19__funct_6])],[e6_19__funct_6,i7_19__funct_6]),
    [interesting(0.8),file(funct_6,i6_19__funct_6),[file(funct_6,i6_19__funct_6)]]).

fof(i5_19__funct_6,plain,(
    ~ ( r2_hidden(c4_19__funct_6,k1_funct_2(k2_zfmisc_1(c1_19__funct_6,c2_19__funct_6),c3_19__funct_6))
      & ~ ( r2_hidden(k3_funct_5(c4_19__funct_6),k1_funct_2(c1_19__funct_6,k1_funct_2(c2_19__funct_6,c3_19__funct_6)))
          & r2_hidden(k5_funct_5(c4_19__funct_6),k1_funct_2(c2_19__funct_6,k1_funct_2(c1_19__funct_6,c3_19__funct_6))) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([e1_19__funct_6,dt_c1_19__funct_6,dt_c2_19__funct_6,dt_c3_19__funct_6,dt_c4_19__funct_6]),discharge_asm(discharge,[e2_19__funct_6])],[e2_19__funct_6,i6_19__funct_6]),
    [interesting(0.8),file(funct_6,i5_19__funct_6),[file(funct_6,i5_19__funct_6)]]).

fof(i4_19__funct_6,plain,
    ( r2_hidden(c4_19__funct_6,k1_funct_2(k2_zfmisc_1(c1_19__funct_6,c2_19__funct_6),c3_19__funct_6))
   => ( k2_zfmisc_1(c1_19__funct_6,c2_19__funct_6) = k1_xboole_0
      | ( r2_hidden(k3_funct_5(c4_19__funct_6),k1_funct_2(c1_19__funct_6,k1_funct_2(c2_19__funct_6,c3_19__funct_6)))
        & r2_hidden(k5_funct_5(c4_19__funct_6),k1_funct_2(c2_19__funct_6,k1_funct_2(c1_19__funct_6,c3_19__funct_6))) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_19__funct_6,dt_c2_19__funct_6,dt_c3_19__funct_6,dt_c4_19__funct_6]),discharge_asm(discharge,[e1_19__funct_6])],[e1_19__funct_6,i5_19__funct_6]),
    [interesting(0.8),file(funct_6,i4_19__funct_6),[file(funct_6,i4_19__funct_6)]]).

fof(i4_19_tmp__funct_6,plain,
    ( ( v1_relat_1(c4_19__funct_6)
      & v1_funct_1(c4_19__funct_6) )
   => ( r2_hidden(c4_19__funct_6,k1_funct_2(k2_zfmisc_1(c1_19__funct_6,c2_19__funct_6),c3_19__funct_6))
     => ( k2_zfmisc_1(c1_19__funct_6,c2_19__funct_6) = k1_xboole_0
        | ( r2_hidden(k3_funct_5(c4_19__funct_6),k1_funct_2(c1_19__funct_6,k1_funct_2(c2_19__funct_6,c3_19__funct_6)))
          & r2_hidden(k5_funct_5(c4_19__funct_6),k1_funct_2(c2_19__funct_6,k1_funct_2(c1_19__funct_6,c3_19__funct_6))) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_19__funct_6,dt_c2_19__funct_6,dt_c3_19__funct_6]),discharge_asm(discharge,[dt_c4_19__funct_6])],[dt_c4_19__funct_6,i4_19__funct_6]),
    [interesting(0.8),i3_19__funct_6]).

fof(i3_19__funct_6,plain,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( r2_hidden(A,k1_funct_2(k2_zfmisc_1(c1_19__funct_6,c2_19__funct_6),c3_19__funct_6))
       => ( k2_zfmisc_1(c1_19__funct_6,c2_19__funct_6) = k1_xboole_0
          | ( r2_hidden(k3_funct_5(A),k1_funct_2(c1_19__funct_6,k1_funct_2(c2_19__funct_6,c3_19__funct_6)))
            & r2_hidden(k5_funct_5(A),k1_funct_2(c2_19__funct_6,k1_funct_2(c1_19__funct_6,c3_19__funct_6))) ) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_19__funct_6,dt_c2_19__funct_6,dt_c3_19__funct_6])],[i4_19_tmp__funct_6,dh_c4_19__funct_6]),
    [interesting(0.8),file(funct_6,i3_19__funct_6),[file(funct_6,i3_19__funct_6)]]).

fof(i3_19_tmp__funct_6,plain,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( r2_hidden(A,k1_funct_2(k2_zfmisc_1(c1_19__funct_6,c2_19__funct_6),c3_19__funct_6))
       => ( k2_zfmisc_1(c1_19__funct_6,c2_19__funct_6) = k1_xboole_0
          | ( r2_hidden(k3_funct_5(A),k1_funct_2(c1_19__funct_6,k1_funct_2(c2_19__funct_6,c3_19__funct_6)))
            & r2_hidden(k5_funct_5(A),k1_funct_2(c2_19__funct_6,k1_funct_2(c1_19__funct_6,c3_19__funct_6))) ) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_19__funct_6,dt_c2_19__funct_6]),discharge_asm(discharge,[dt_c3_19__funct_6])],[dt_c3_19__funct_6,i3_19__funct_6]),
    [interesting(0.8),i2_19__funct_6]).

fof(i2_19__funct_6,plain,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( r2_hidden(B,k1_funct_2(k2_zfmisc_1(c1_19__funct_6,c2_19__funct_6),A))
       => ( k2_zfmisc_1(c1_19__funct_6,c2_19__funct_6) = k1_xboole_0
          | ( r2_hidden(k3_funct_5(B),k1_funct_2(c1_19__funct_6,k1_funct_2(c2_19__funct_6,A)))
            & r2_hidden(k5_funct_5(B),k1_funct_2(c2_19__funct_6,k1_funct_2(c1_19__funct_6,A))) ) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_19__funct_6,dt_c2_19__funct_6])],[i3_19_tmp__funct_6,dh_c3_19__funct_6]),
    [interesting(0.8),file(funct_6,i2_19__funct_6),[file(funct_6,i2_19__funct_6)]]).

fof(i2_19_tmp__funct_6,plain,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( r2_hidden(B,k1_funct_2(k2_zfmisc_1(c1_19__funct_6,c2_19__funct_6),A))
       => ( k2_zfmisc_1(c1_19__funct_6,c2_19__funct_6) = k1_xboole_0
          | ( r2_hidden(k3_funct_5(B),k1_funct_2(c1_19__funct_6,k1_funct_2(c2_19__funct_6,A)))
            & r2_hidden(k5_funct_5(B),k1_funct_2(c2_19__funct_6,k1_funct_2(c1_19__funct_6,A))) ) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_19__funct_6]),discharge_asm(discharge,[dt_c2_19__funct_6])],[dt_c2_19__funct_6,i2_19__funct_6]),
    [interesting(0.8),i1_19__funct_6]).

fof(i1_19__funct_6,plain,(
    ! [A,B,C] : 
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ( r2_hidden(C,k1_funct_2(k2_zfmisc_1(c1_19__funct_6,A),B))
       => ( k2_zfmisc_1(c1_19__funct_6,A) = k1_xboole_0
          | ( r2_hidden(k3_funct_5(C),k1_funct_2(c1_19__funct_6,k1_funct_2(A,B)))
            & r2_hidden(k5_funct_5(C),k1_funct_2(A,k1_funct_2(c1_19__funct_6,B))) ) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_19__funct_6])],[i2_19_tmp__funct_6,dh_c2_19__funct_6]),
    [interesting(0.8),file(funct_6,i1_19__funct_6),[file(funct_6,i1_19__funct_6)]]).

fof(i1_19_tmp__funct_6,plain,(
    ! [A,B,C] : 
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ( r2_hidden(C,k1_funct_2(k2_zfmisc_1(c1_19__funct_6,A),B))
       => ( k2_zfmisc_1(c1_19__funct_6,A) = k1_xboole_0
          | ( r2_hidden(k3_funct_5(C),k1_funct_2(c1_19__funct_6,k1_funct_2(A,B)))
            & r2_hidden(k5_funct_5(C),k1_funct_2(A,k1_funct_2(c1_19__funct_6,B))) ) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_19__funct_6])],[dt_c1_19__funct_6,i1_19__funct_6]),
    [interesting(1),t19_funct_6]).

fof(t19_funct_6,theorem,(
    ! [A,B,C,D] : 
      ( ( v1_relat_1(D)
        & v1_funct_1(D) )
     => ( r2_hidden(D,k1_funct_2(k2_zfmisc_1(A,B),C))
       => ( k2_zfmisc_1(A,B) = k1_xboole_0
          | ( r2_hidden(k3_funct_5(D),k1_funct_2(A,k1_funct_2(B,C)))
            & r2_hidden(k5_funct_5(D),k1_funct_2(B,k1_funct_2(A,C))) ) ) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_19_tmp__funct_6,dh_c1_19__funct_6]),
    [interesting(1),file(funct_6,t19_funct_6),[file(funct_6,t19_funct_6)]]).