% Mizar ND problem: t3_funct_7,funct_7,61,11 
fof(dh_c1_3__funct_7,definition,
    ( ( ~ v1_xboole_0(c1_3__funct_7)
     => ! [A] : 
          ( ~ v1_xboole_0(A)
         => ! [B] : 
              ( ( v1_funct_1(B)
                & v1_funct_2(B,c1_3__funct_7,A)
                & m2_relset_1(B,c1_3__funct_7,A) )
             => ( v2_funct_1(B)
               => ! [C] : 
                    ( m1_subset_1(C,c1_3__funct_7)
                   => ! [D] : 
                        ( m1_subset_1(D,k1_zfmisc_1(c1_3__funct_7))
                       => ( r2_hidden(k8_funct_2(c1_3__funct_7,A,B,C),k2_funct_2(c1_3__funct_7,A,B,D))
                         => r2_hidden(C,D) ) ) ) ) ) ) )
   => ! [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) )
               => ( v2_funct_1(G)
                 => ! [H] : 
                      ( m1_subset_1(H,E)
                     => ! [I] : 
                          ( m1_subset_1(I,k1_zfmisc_1(E))
                         => ( r2_hidden(k8_funct_2(E,F,G,H),k2_funct_2(E,F,G,I))
                           => r2_hidden(H,I) ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbol(c1_3__funct_7),file(funct_7,c1_3__funct_7)]),
    [interesting(0.8),axiom,file(funct_7,c1_3__funct_7)]).

fof(dh_c2_3__funct_7,definition,
    ( ( ~ v1_xboole_0(c2_3__funct_7)
     => ! [A] : 
          ( ( v1_funct_1(A)
            & v1_funct_2(A,c1_3__funct_7,c2_3__funct_7)
            & m2_relset_1(A,c1_3__funct_7,c2_3__funct_7) )
         => ( v2_funct_1(A)
           => ! [B] : 
                ( m1_subset_1(B,c1_3__funct_7)
               => ! [C] : 
                    ( m1_subset_1(C,k1_zfmisc_1(c1_3__funct_7))
                   => ( r2_hidden(k8_funct_2(c1_3__funct_7,c2_3__funct_7,A,B),k2_funct_2(c1_3__funct_7,c2_3__funct_7,A,C))
                     => r2_hidden(B,C) ) ) ) ) ) )
   => ! [D] : 
        ( ~ v1_xboole_0(D)
       => ! [E] : 
            ( ( v1_funct_1(E)
              & v1_funct_2(E,c1_3__funct_7,D)
              & m2_relset_1(E,c1_3__funct_7,D) )
           => ( v2_funct_1(E)
             => ! [F] : 
                  ( m1_subset_1(F,c1_3__funct_7)
                 => ! [G] : 
                      ( m1_subset_1(G,k1_zfmisc_1(c1_3__funct_7))
                     => ( r2_hidden(k8_funct_2(c1_3__funct_7,D,E,F),k2_funct_2(c1_3__funct_7,D,E,G))
                       => r2_hidden(F,G) ) ) ) ) ) ) ),
    introduced(definition,[new_symbol(c2_3__funct_7),file(funct_7,c2_3__funct_7)]),
    [interesting(0.8),axiom,file(funct_7,c2_3__funct_7)]).

fof(dh_c3_3__funct_7,definition,
    ( ( ( v1_funct_1(c3_3__funct_7)
        & v1_funct_2(c3_3__funct_7,c1_3__funct_7,c2_3__funct_7)
        & m2_relset_1(c3_3__funct_7,c1_3__funct_7,c2_3__funct_7) )
     => ( v2_funct_1(c3_3__funct_7)
       => ! [A] : 
            ( m1_subset_1(A,c1_3__funct_7)
           => ! [B] : 
                ( m1_subset_1(B,k1_zfmisc_1(c1_3__funct_7))
               => ( r2_hidden(k8_funct_2(c1_3__funct_7,c2_3__funct_7,c3_3__funct_7,A),k2_funct_2(c1_3__funct_7,c2_3__funct_7,c3_3__funct_7,B))
                 => r2_hidden(A,B) ) ) ) ) )
   => ! [C] : 
        ( ( v1_funct_1(C)
          & v1_funct_2(C,c1_3__funct_7,c2_3__funct_7)
          & m2_relset_1(C,c1_3__funct_7,c2_3__funct_7) )
       => ( v2_funct_1(C)
         => ! [D] : 
              ( m1_subset_1(D,c1_3__funct_7)
             => ! [E] : 
                  ( m1_subset_1(E,k1_zfmisc_1(c1_3__funct_7))
                 => ( r2_hidden(k8_funct_2(c1_3__funct_7,c2_3__funct_7,C,D),k2_funct_2(c1_3__funct_7,c2_3__funct_7,C,E))
                   => r2_hidden(D,E) ) ) ) ) ) ),
    introduced(definition,[new_symbol(c3_3__funct_7),file(funct_7,c3_3__funct_7)]),
    [interesting(0.8),axiom,file(funct_7,c3_3__funct_7)]).

fof(e1_3__funct_7,assumption,(
    v2_funct_1(c3_3__funct_7) ),
    introduced(assumption,[file(funct_7,e1_3__funct_7)]),
    [interesting(0.8),axiom,file(funct_7,e1_3__funct_7)]).

fof(dh_c4_3__funct_7,definition,
    ( ( m1_subset_1(c4_3__funct_7,c1_3__funct_7)
     => ! [A] : 
          ( m1_subset_1(A,k1_zfmisc_1(c1_3__funct_7))
         => ( r2_hidden(k8_funct_2(c1_3__funct_7,c2_3__funct_7,c3_3__funct_7,c4_3__funct_7),k2_funct_2(c1_3__funct_7,c2_3__funct_7,c3_3__funct_7,A))
           => r2_hidden(c4_3__funct_7,A) ) ) )
   => ! [B] : 
        ( m1_subset_1(B,c1_3__funct_7)
       => ! [C] : 
            ( m1_subset_1(C,k1_zfmisc_1(c1_3__funct_7))
           => ( r2_hidden(k8_funct_2(c1_3__funct_7,c2_3__funct_7,c3_3__funct_7,B),k2_funct_2(c1_3__funct_7,c2_3__funct_7,c3_3__funct_7,C))
             => r2_hidden(B,C) ) ) ) ),
    introduced(definition,[new_symbol(c4_3__funct_7),file(funct_7,c4_3__funct_7)]),
    [interesting(0.8),axiom,file(funct_7,c4_3__funct_7)]).

fof(dh_c5_3__funct_7,definition,
    ( ( m1_subset_1(c5_3__funct_7,k1_zfmisc_1(c1_3__funct_7))
     => ( r2_hidden(k8_funct_2(c1_3__funct_7,c2_3__funct_7,c3_3__funct_7,c4_3__funct_7),k2_funct_2(c1_3__funct_7,c2_3__funct_7,c3_3__funct_7,c5_3__funct_7))
       => r2_hidden(c4_3__funct_7,c5_3__funct_7) ) )
   => ! [A] : 
        ( m1_subset_1(A,k1_zfmisc_1(c1_3__funct_7))
       => ( r2_hidden(k8_funct_2(c1_3__funct_7,c2_3__funct_7,c3_3__funct_7,c4_3__funct_7),k2_funct_2(c1_3__funct_7,c2_3__funct_7,c3_3__funct_7,A))
         => r2_hidden(c4_3__funct_7,A) ) ) ),
    introduced(definition,[new_symbol(c5_3__funct_7),file(funct_7,c5_3__funct_7)]),
    [interesting(0.8),axiom,file(funct_7,c5_3__funct_7)]).

fof(e2_3__funct_7,assumption,(
    r2_hidden(k8_funct_2(c1_3__funct_7,c2_3__funct_7,c3_3__funct_7,c4_3__funct_7),k2_funct_2(c1_3__funct_7,c2_3__funct_7,c3_3__funct_7,c5_3__funct_7)) ),
    introduced(assumption,[file(funct_7,e2_3__funct_7)]),
    [interesting(0.8),axiom,file(funct_7,e2_3__funct_7)]).

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

fof(existence_m1_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_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(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_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(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(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_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(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_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(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(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(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(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(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(antisymmetry_r2_hidden,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => ~ r2_hidden(B,A) ) ),
    file(hidden,r2_hidden),
    [interesting(0.9),axiom,file(hidden,r2_hidden)]).

fof(existence_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_k8_funct_2,definition,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B)
        & m1_subset_1(D,A) )
     => k8_funct_2(A,B,C,D) = k1_funct_1(C,D) ) ),
    file(funct_2,k8_funct_2),
    [interesting(0.9),axiom,file(funct_2,k8_funct_2)]).

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_1,axiom,(
    $true ),
    file(funct_1,k1_funct_1),
    [interesting(0.9),axiom,file(funct_1,k1_funct_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_k8_funct_2,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B)
        & m1_subset_1(D,A) )
     => m1_subset_1(k8_funct_2(A,B,C,D),B) ) ),
    file(funct_2,k8_funct_2),
    [interesting(0.9),axiom,file(funct_2,k8_funct_2)]).

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_3__funct_7,assumption,(
    ~ v1_xboole_0(c1_3__funct_7) ),
    introduced(assumption,[file(funct_7,c1_3__funct_7)]),
    [interesting(0.8),axiom,file(funct_7,c1_3__funct_7)]).

fof(dt_c2_3__funct_7,assumption,(
    ~ v1_xboole_0(c2_3__funct_7) ),
    introduced(assumption,[file(funct_7,c2_3__funct_7)]),
    [interesting(0.8),axiom,file(funct_7,c2_3__funct_7)]).

fof(dt_c3_3__funct_7,assumption,
    ( v1_funct_1(c3_3__funct_7)
    & v1_funct_2(c3_3__funct_7,c1_3__funct_7,c2_3__funct_7)
    & m2_relset_1(c3_3__funct_7,c1_3__funct_7,c2_3__funct_7) ),
    introduced(assumption,[file(funct_7,c3_3__funct_7)]),
    [interesting(0.8),axiom,file(funct_7,c3_3__funct_7)]).

fof(dt_c4_3__funct_7,assumption,(
    m1_subset_1(c4_3__funct_7,c1_3__funct_7) ),
    introduced(assumption,[file(funct_7,c4_3__funct_7)]),
    [interesting(0.8),axiom,file(funct_7,c4_3__funct_7)]).

fof(dt_c5_3__funct_7,assumption,(
    m1_subset_1(c5_3__funct_7,k1_zfmisc_1(c1_3__funct_7)) ),
    introduced(assumption,[file(funct_7,c5_3__funct_7)]),
    [interesting(0.8),axiom,file(funct_7,c5_3__funct_7)]).

fof(dh_c6_3__funct_7,definition,
    ( ? [A] : 
        ( m1_subset_1(A,c1_3__funct_7)
        & r2_hidden(A,c5_3__funct_7)
        & k8_funct_2(c1_3__funct_7,c2_3__funct_7,c3_3__funct_7,A) = k8_funct_2(c1_3__funct_7,c2_3__funct_7,c3_3__funct_7,c4_3__funct_7) )
   => ( m1_subset_1(c6_3__funct_7,c1_3__funct_7)
      & r2_hidden(c6_3__funct_7,c5_3__funct_7)
      & k8_funct_2(c1_3__funct_7,c2_3__funct_7,c3_3__funct_7,c6_3__funct_7) = k8_funct_2(c1_3__funct_7,c2_3__funct_7,c3_3__funct_7,c4_3__funct_7) ) ),
    introduced(definition,[new_symbol(c6_3__funct_7),file(funct_7,c6_3__funct_7)]),
    [interesting(0.8),axiom,file(funct_7,c6_3__funct_7)]).

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(dt_k9_relat_1,axiom,(
    $true ),
    file(relat_1,k9_relat_1),
    [interesting(0.9),axiom,file(relat_1,k9_relat_1)]).

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(redefinition_k2_funct_2,definition,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B) )
     => k2_funct_2(A,B,C,D) = k9_relat_1(C,D) ) ),
    file(funct_2,k2_funct_2),
    [interesting(0.9),axiom,file(funct_2,k2_funct_2)]).

fof(dt_k2_funct_2,axiom,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B) )
     => m1_subset_1(k2_funct_2(A,B,C,D),k1_zfmisc_1(B)) ) ),
    file(funct_2,k2_funct_2),
    [interesting(0.9),axiom,file(funct_2,k2_funct_2)]).

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(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(t116_funct_2,theorem,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m2_relset_1(D,A,B) )
     => ! [E] : 
          ~ ( r2_hidden(E,k2_funct_2(A,B,D,C))
            & ! [F] : 
                ( m1_subset_1(F,A)
               => ~ ( r2_hidden(F,C)
                    & E = k1_funct_1(D,F) ) ) ) ) ),
    file(funct_2,t116_funct_2),
    [interesting(0.9),axiom,file(funct_2,t116_funct_2)]).

fof(e3_3__funct_7,plain,(
    ? [A] : 
      ( m1_subset_1(A,c1_3__funct_7)
      & r2_hidden(A,c5_3__funct_7)
      & k8_funct_2(c1_3__funct_7,c2_3__funct_7,c3_3__funct_7,A) = k8_funct_2(c1_3__funct_7,c2_3__funct_7,c3_3__funct_7,c4_3__funct_7) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__funct_7,dt_c2_3__funct_7,dt_c3_3__funct_7,dt_c4_3__funct_7,dt_c5_3__funct_7,e2_3__funct_7])],[cc1_finseq_1,rc1_finseq_1,rc3_finseq_1,rc3_relat_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,reflexivity_r1_tarski,dt_k1_xboole_0,fc12_relat_1,fc2_finseq_1,fc4_relat_1,rc1_partfun1,rc3_funct_1,existence_m1_relset_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k9_relat_1,dt_m1_relset_1,cc1_funct_1,cc1_relat_1,cc1_relset_1,cc2_funct_1,fc1_subset_1,fc4_subset_1,rc1_funct_1,rc1_relat_1,rc1_subset_1,rc2_funct_1,rc2_partfun1,rc2_relat_1,rc2_subset_1,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,existence_m1_subset_1,existence_m2_relset_1,redefinition_k2_funct_2,redefinition_k8_funct_2,redefinition_m2_relset_1,dt_k1_funct_1,dt_k2_funct_2,dt_k8_funct_2,dt_m1_subset_1,dt_m2_relset_1,dt_c1_3__funct_7,dt_c2_3__funct_7,dt_c3_3__funct_7,dt_c4_3__funct_7,dt_c5_3__funct_7,t1_subset,t7_boole,e2_3__funct_7,t116_funct_2]),
    [interesting(0.8),file(funct_7,e3_3__funct_7),[file(funct_7,e3_3__funct_7)]]).

fof(dt_c6_3__funct_7,plain,(
    m1_subset_1(c6_3__funct_7,c1_3__funct_7) ),
    inference(consider,[status(thm),assumptions([dt_c1_3__funct_7,dt_c2_3__funct_7,dt_c3_3__funct_7,dt_c4_3__funct_7,dt_c5_3__funct_7,e2_3__funct_7])],[dh_c6_3__funct_7,e3_3__funct_7]),
    [interesting(0.8),file(funct_7,c6_3__funct_7),[file(funct_7,c6_3__funct_7)]]).

fof(e4_3__funct_7,plain,(
    r2_hidden(c6_3__funct_7,c5_3__funct_7) ),
    inference(consider,[status(thm),assumptions([dt_c1_3__funct_7,dt_c2_3__funct_7,dt_c3_3__funct_7,dt_c4_3__funct_7,dt_c5_3__funct_7,e2_3__funct_7])],[dh_c6_3__funct_7,e3_3__funct_7]),
    [interesting(0.8),file(funct_7,e4_3__funct_7),[file(funct_7,e4_3__funct_7)]]).

fof(e5_3__funct_7,plain,(
    k8_funct_2(c1_3__funct_7,c2_3__funct_7,c3_3__funct_7,c6_3__funct_7) = k8_funct_2(c1_3__funct_7,c2_3__funct_7,c3_3__funct_7,c4_3__funct_7) ),
    inference(consider,[status(thm),assumptions([dt_c1_3__funct_7,dt_c2_3__funct_7,dt_c3_3__funct_7,dt_c4_3__funct_7,dt_c5_3__funct_7,e2_3__funct_7])],[dh_c6_3__funct_7,e3_3__funct_7]),
    [interesting(0.8),file(funct_7,e5_3__funct_7),[file(funct_7,e5_3__funct_7)]]).

fof(t25_funct_2,theorem,(
    ! [A,B,C] : 
      ( ( v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m2_relset_1(C,A,B) )
     => ( ( B = k1_xboole_0
         => A = k1_xboole_0 )
       => ( v2_funct_1(C)
        <=> ! [D,E] : 
              ( ( r2_hidden(D,A)
                & r2_hidden(E,A)
                & k1_funct_1(C,D) = k1_funct_1(C,E) )
             => D = E ) ) ) ) ),
    file(funct_2,t25_funct_2),
    [interesting(0.9),axiom,file(funct_2,t25_funct_2)]).

fof(e6_3__funct_7,plain,(
    r2_hidden(c4_3__funct_7,c5_3__funct_7) ),
    inference(mizar_by,[status(thm),assumptions([e1_3__funct_7,dt_c1_3__funct_7,dt_c2_3__funct_7,dt_c3_3__funct_7,dt_c4_3__funct_7,dt_c5_3__funct_7,e2_3__funct_7])],[reflexivity_r1_tarski,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_funct_1,cc1_relat_1,cc1_relset_1,cc2_funct_1,fc1_subset_1,fc4_subset_1,rc1_finseq_1,rc1_funct_1,rc1_partfun1,rc1_relat_1,rc1_subset_1,rc2_funct_1,rc2_partfun1,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,t3_subset,t4_subset,t5_subset,t8_boole,antisymmetry_r2_hidden,existence_m2_relset_1,redefinition_k8_funct_2,redefinition_m2_relset_1,dt_k1_funct_1,dt_k1_xboole_0,dt_k8_funct_2,dt_m2_relset_1,dt_c1_3__funct_7,dt_c2_3__funct_7,dt_c3_3__funct_7,dt_c4_3__funct_7,dt_c5_3__funct_7,dt_c6_3__funct_7,fc12_relat_1,fc2_finseq_1,fc4_relat_1,t1_subset,t6_boole,t7_boole,e1_3__funct_7,e4_3__funct_7,e5_3__funct_7,t25_funct_2]),
    [interesting(0.8),file(funct_7,e6_3__funct_7),[file(funct_7,e6_3__funct_7)]]).

fof(i7_3__funct_7,theorem,(
    $true ),
    introduced(tautology,[file(funct_7,i7_3__funct_7)]),
    [interesting(0.8),trivial,file(funct_7,i7_3__funct_7)]).

fof(i6_3__funct_7,plain,(
    r2_hidden(c4_3__funct_7,c5_3__funct_7) ),
    inference(conclusion,[status(thm),assumptions([e1_3__funct_7,dt_c1_3__funct_7,dt_c2_3__funct_7,dt_c3_3__funct_7,dt_c4_3__funct_7,dt_c5_3__funct_7,e2_3__funct_7])],[e6_3__funct_7,i7_3__funct_7]),
    [interesting(0.8),file(funct_7,i6_3__funct_7),[file(funct_7,i6_3__funct_7)]]).

fof(i5_3__funct_7,plain,
    ( r2_hidden(k8_funct_2(c1_3__funct_7,c2_3__funct_7,c3_3__funct_7,c4_3__funct_7),k2_funct_2(c1_3__funct_7,c2_3__funct_7,c3_3__funct_7,c5_3__funct_7))
   => r2_hidden(c4_3__funct_7,c5_3__funct_7) ),
    inference(discharge_asm,[status(thm),assumptions([e1_3__funct_7,dt_c1_3__funct_7,dt_c2_3__funct_7,dt_c3_3__funct_7,dt_c4_3__funct_7,dt_c5_3__funct_7]),discharge_asm(discharge,[e2_3__funct_7])],[e2_3__funct_7,i6_3__funct_7]),
    [interesting(0.8),file(funct_7,i5_3__funct_7),[file(funct_7,i5_3__funct_7)]]).

fof(i5_3_tmp__funct_7,plain,
    ( m1_subset_1(c5_3__funct_7,k1_zfmisc_1(c1_3__funct_7))
   => ( r2_hidden(k8_funct_2(c1_3__funct_7,c2_3__funct_7,c3_3__funct_7,c4_3__funct_7),k2_funct_2(c1_3__funct_7,c2_3__funct_7,c3_3__funct_7,c5_3__funct_7))
     => r2_hidden(c4_3__funct_7,c5_3__funct_7) ) ),
    inference(discharge_asm,[status(thm),assumptions([e1_3__funct_7,dt_c1_3__funct_7,dt_c2_3__funct_7,dt_c3_3__funct_7,dt_c4_3__funct_7]),discharge_asm(discharge,[dt_c5_3__funct_7])],[dt_c5_3__funct_7,i5_3__funct_7]),
    [interesting(0.8),i4_3__funct_7]).

fof(i4_3__funct_7,plain,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(c1_3__funct_7))
     => ( r2_hidden(k8_funct_2(c1_3__funct_7,c2_3__funct_7,c3_3__funct_7,c4_3__funct_7),k2_funct_2(c1_3__funct_7,c2_3__funct_7,c3_3__funct_7,A))
       => r2_hidden(c4_3__funct_7,A) ) ) ),
    inference(let,[status(thm),assumptions([e1_3__funct_7,dt_c1_3__funct_7,dt_c2_3__funct_7,dt_c3_3__funct_7,dt_c4_3__funct_7])],[i5_3_tmp__funct_7,dh_c5_3__funct_7]),
    [interesting(0.8),file(funct_7,i4_3__funct_7),[file(funct_7,i4_3__funct_7)]]).

fof(i4_3_tmp__funct_7,plain,
    ( m1_subset_1(c4_3__funct_7,c1_3__funct_7)
   => ! [A] : 
        ( m1_subset_1(A,k1_zfmisc_1(c1_3__funct_7))
       => ( r2_hidden(k8_funct_2(c1_3__funct_7,c2_3__funct_7,c3_3__funct_7,c4_3__funct_7),k2_funct_2(c1_3__funct_7,c2_3__funct_7,c3_3__funct_7,A))
         => r2_hidden(c4_3__funct_7,A) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([e1_3__funct_7,dt_c1_3__funct_7,dt_c2_3__funct_7,dt_c3_3__funct_7]),discharge_asm(discharge,[dt_c4_3__funct_7])],[dt_c4_3__funct_7,i4_3__funct_7]),
    [interesting(0.8),i3_3__funct_7]).

fof(i3_3__funct_7,plain,(
    ! [A] : 
      ( m1_subset_1(A,c1_3__funct_7)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(c1_3__funct_7))
         => ( r2_hidden(k8_funct_2(c1_3__funct_7,c2_3__funct_7,c3_3__funct_7,A),k2_funct_2(c1_3__funct_7,c2_3__funct_7,c3_3__funct_7,B))
           => r2_hidden(A,B) ) ) ) ),
    inference(let,[status(thm),assumptions([e1_3__funct_7,dt_c1_3__funct_7,dt_c2_3__funct_7,dt_c3_3__funct_7])],[i4_3_tmp__funct_7,dh_c4_3__funct_7]),
    [interesting(0.8),file(funct_7,i3_3__funct_7),[file(funct_7,i3_3__funct_7)]]).

fof(i2_3__funct_7,plain,
    ( v2_funct_1(c3_3__funct_7)
   => ! [A] : 
        ( m1_subset_1(A,c1_3__funct_7)
       => ! [B] : 
            ( m1_subset_1(B,k1_zfmisc_1(c1_3__funct_7))
           => ( r2_hidden(k8_funct_2(c1_3__funct_7,c2_3__funct_7,c3_3__funct_7,A),k2_funct_2(c1_3__funct_7,c2_3__funct_7,c3_3__funct_7,B))
             => r2_hidden(A,B) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3__funct_7,dt_c2_3__funct_7,dt_c3_3__funct_7]),discharge_asm(discharge,[e1_3__funct_7])],[e1_3__funct_7,i3_3__funct_7]),
    [interesting(0.8),file(funct_7,i2_3__funct_7),[file(funct_7,i2_3__funct_7)]]).

fof(i2_3_tmp__funct_7,plain,
    ( ( v1_funct_1(c3_3__funct_7)
      & v1_funct_2(c3_3__funct_7,c1_3__funct_7,c2_3__funct_7)
      & m2_relset_1(c3_3__funct_7,c1_3__funct_7,c2_3__funct_7) )
   => ( v2_funct_1(c3_3__funct_7)
     => ! [A] : 
          ( m1_subset_1(A,c1_3__funct_7)
         => ! [B] : 
              ( m1_subset_1(B,k1_zfmisc_1(c1_3__funct_7))
             => ( r2_hidden(k8_funct_2(c1_3__funct_7,c2_3__funct_7,c3_3__funct_7,A),k2_funct_2(c1_3__funct_7,c2_3__funct_7,c3_3__funct_7,B))
               => r2_hidden(A,B) ) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3__funct_7,dt_c2_3__funct_7]),discharge_asm(discharge,[dt_c3_3__funct_7])],[dt_c3_3__funct_7,i2_3__funct_7]),
    [interesting(0.8),i1_3__funct_7]).

fof(i1_3__funct_7,plain,(
    ! [A] : 
      ( ( v1_funct_1(A)
        & v1_funct_2(A,c1_3__funct_7,c2_3__funct_7)
        & m2_relset_1(A,c1_3__funct_7,c2_3__funct_7) )
     => ( v2_funct_1(A)
       => ! [B] : 
            ( m1_subset_1(B,c1_3__funct_7)
           => ! [C] : 
                ( m1_subset_1(C,k1_zfmisc_1(c1_3__funct_7))
               => ( r2_hidden(k8_funct_2(c1_3__funct_7,c2_3__funct_7,A,B),k2_funct_2(c1_3__funct_7,c2_3__funct_7,A,C))
                 => r2_hidden(B,C) ) ) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_3__funct_7,dt_c2_3__funct_7])],[i2_3_tmp__funct_7,dh_c3_3__funct_7]),
    [interesting(0.8),file(funct_7,i1_3__funct_7),[file(funct_7,i1_3__funct_7)]]).

fof(i1_3_tmp__funct_7,plain,
    ( ( ~ v1_xboole_0(c1_3__funct_7)
      & ~ v1_xboole_0(c2_3__funct_7) )
   => ! [A] : 
        ( ( v1_funct_1(A)
          & v1_funct_2(A,c1_3__funct_7,c2_3__funct_7)
          & m2_relset_1(A,c1_3__funct_7,c2_3__funct_7) )
       => ( v2_funct_1(A)
         => ! [B] : 
              ( m1_subset_1(B,c1_3__funct_7)
             => ! [C] : 
                  ( m1_subset_1(C,k1_zfmisc_1(c1_3__funct_7))
                 => ( r2_hidden(k8_funct_2(c1_3__funct_7,c2_3__funct_7,A,B),k2_funct_2(c1_3__funct_7,c2_3__funct_7,A,C))
                   => r2_hidden(B,C) ) ) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_3__funct_7,dt_c2_3__funct_7])],[dt_c1_3__funct_7,dt_c2_3__funct_7,i1_3__funct_7]),
    [interesting(1),t3_funct_7]).

fof(t3_funct_7,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) )
             => ( v2_funct_1(C)
               => ! [D] : 
                    ( m1_subset_1(D,A)
                   => ! [E] : 
                        ( m1_subset_1(E,k1_zfmisc_1(A))
                       => ( r2_hidden(k8_funct_2(A,B,C,D),k2_funct_2(A,B,C,E))
                         => r2_hidden(D,E) ) ) ) ) ) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_3_tmp__funct_7,dh_c1_3__funct_7,dh_c2_3__funct_7]),
    [interesting(1),file(funct_7,t3_funct_7),[file(funct_7,t3_funct_7)]]).