% Mizar ND problem: t5_funct_7,funct_7,95,22 
fof(dh_c1_5__funct_7,definition,
    ( ( ~ v1_xboole_0(c1_5__funct_7)
     => ! [A] : 
          ( ~ v1_xboole_0(A)
         => ! [B] : 
              ( ( v1_funct_1(B)
                & v1_funct_2(B,c1_5__funct_7,A)
                & m2_relset_1(B,c1_5__funct_7,A) )
             => ( v2_funct_1(B)
               => ! [C] : 
                    ( m1_subset_1(C,A)
                   => ! [D] : 
                        ( m1_subset_1(D,k1_zfmisc_1(c1_5__funct_7))
                       => ! [E] : 
                            ( m1_subset_1(E,k1_zfmisc_1(A))
                           => ( r2_hidden(C,k6_subset_1(A,k2_funct_2(c1_5__funct_7,A,B,D),E))
                             => r2_hidden(k1_funct_1(k2_funct_1(B),C),k6_subset_1(c1_5__funct_7,D,k3_funct_2(c1_5__funct_7,A,B,E))) ) ) ) ) ) ) ) )
   => ! [F] : 
        ( ~ v1_xboole_0(F)
       => ! [G] : 
            ( ~ v1_xboole_0(G)
           => ! [H] : 
                ( ( v1_funct_1(H)
                  & v1_funct_2(H,F,G)
                  & m2_relset_1(H,F,G) )
               => ( v2_funct_1(H)
                 => ! [I] : 
                      ( m1_subset_1(I,G)
                     => ! [J] : 
                          ( m1_subset_1(J,k1_zfmisc_1(F))
                         => ! [K] : 
                              ( m1_subset_1(K,k1_zfmisc_1(G))
                             => ( r2_hidden(I,k6_subset_1(G,k2_funct_2(F,G,H,J),K))
                               => r2_hidden(k1_funct_1(k2_funct_1(H),I),k6_subset_1(F,J,k3_funct_2(F,G,H,K))) ) ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbol(c1_5__funct_7),file(funct_7,c1_5__funct_7)]),
    [interesting(0.8),axiom,file(funct_7,c1_5__funct_7)]).

fof(dh_c2_5__funct_7,definition,
    ( ( ~ v1_xboole_0(c2_5__funct_7)
     => ! [A] : 
          ( ( v1_funct_1(A)
            & v1_funct_2(A,c1_5__funct_7,c2_5__funct_7)
            & m2_relset_1(A,c1_5__funct_7,c2_5__funct_7) )
         => ( v2_funct_1(A)
           => ! [B] : 
                ( m1_subset_1(B,c2_5__funct_7)
               => ! [C] : 
                    ( m1_subset_1(C,k1_zfmisc_1(c1_5__funct_7))
                   => ! [D] : 
                        ( m1_subset_1(D,k1_zfmisc_1(c2_5__funct_7))
                       => ( r2_hidden(B,k6_subset_1(c2_5__funct_7,k2_funct_2(c1_5__funct_7,c2_5__funct_7,A,C),D))
                         => r2_hidden(k1_funct_1(k2_funct_1(A),B),k6_subset_1(c1_5__funct_7,C,k3_funct_2(c1_5__funct_7,c2_5__funct_7,A,D))) ) ) ) ) ) ) )
   => ! [E] : 
        ( ~ v1_xboole_0(E)
       => ! [F] : 
            ( ( v1_funct_1(F)
              & v1_funct_2(F,c1_5__funct_7,E)
              & m2_relset_1(F,c1_5__funct_7,E) )
           => ( v2_funct_1(F)
             => ! [G] : 
                  ( m1_subset_1(G,E)
                 => ! [H] : 
                      ( m1_subset_1(H,k1_zfmisc_1(c1_5__funct_7))
                     => ! [I] : 
                          ( m1_subset_1(I,k1_zfmisc_1(E))
                         => ( r2_hidden(G,k6_subset_1(E,k2_funct_2(c1_5__funct_7,E,F,H),I))
                           => r2_hidden(k1_funct_1(k2_funct_1(F),G),k6_subset_1(c1_5__funct_7,H,k3_funct_2(c1_5__funct_7,E,F,I))) ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbol(c2_5__funct_7),file(funct_7,c2_5__funct_7)]),
    [interesting(0.8),axiom,file(funct_7,c2_5__funct_7)]).

fof(dh_c3_5__funct_7,definition,
    ( ( ( v1_funct_1(c3_5__funct_7)
        & v1_funct_2(c3_5__funct_7,c1_5__funct_7,c2_5__funct_7)
        & m2_relset_1(c3_5__funct_7,c1_5__funct_7,c2_5__funct_7) )
     => ( v2_funct_1(c3_5__funct_7)
       => ! [A] : 
            ( m1_subset_1(A,c2_5__funct_7)
           => ! [B] : 
                ( m1_subset_1(B,k1_zfmisc_1(c1_5__funct_7))
               => ! [C] : 
                    ( m1_subset_1(C,k1_zfmisc_1(c2_5__funct_7))
                   => ( r2_hidden(A,k6_subset_1(c2_5__funct_7,k2_funct_2(c1_5__funct_7,c2_5__funct_7,c3_5__funct_7,B),C))
                     => r2_hidden(k1_funct_1(k2_funct_1(c3_5__funct_7),A),k6_subset_1(c1_5__funct_7,B,k3_funct_2(c1_5__funct_7,c2_5__funct_7,c3_5__funct_7,C))) ) ) ) ) ) )
   => ! [D] : 
        ( ( v1_funct_1(D)
          & v1_funct_2(D,c1_5__funct_7,c2_5__funct_7)
          & m2_relset_1(D,c1_5__funct_7,c2_5__funct_7) )
       => ( v2_funct_1(D)
         => ! [E] : 
              ( m1_subset_1(E,c2_5__funct_7)
             => ! [F] : 
                  ( m1_subset_1(F,k1_zfmisc_1(c1_5__funct_7))
                 => ! [G] : 
                      ( m1_subset_1(G,k1_zfmisc_1(c2_5__funct_7))
                     => ( r2_hidden(E,k6_subset_1(c2_5__funct_7,k2_funct_2(c1_5__funct_7,c2_5__funct_7,D,F),G))
                       => r2_hidden(k1_funct_1(k2_funct_1(D),E),k6_subset_1(c1_5__funct_7,F,k3_funct_2(c1_5__funct_7,c2_5__funct_7,D,G))) ) ) ) ) ) ) ),
    introduced(definition,[new_symbol(c3_5__funct_7),file(funct_7,c3_5__funct_7)]),
    [interesting(0.8),axiom,file(funct_7,c3_5__funct_7)]).

fof(e1_5__funct_7,assumption,(
    v2_funct_1(c3_5__funct_7) ),
    introduced(assumption,[file(funct_7,e1_5__funct_7)]),
    [interesting(0.8),axiom,file(funct_7,e1_5__funct_7)]).

fof(dh_c4_5__funct_7,definition,
    ( ( m1_subset_1(c4_5__funct_7,c2_5__funct_7)
     => ! [A] : 
          ( m1_subset_1(A,k1_zfmisc_1(c1_5__funct_7))
         => ! [B] : 
              ( m1_subset_1(B,k1_zfmisc_1(c2_5__funct_7))
             => ( r2_hidden(c4_5__funct_7,k6_subset_1(c2_5__funct_7,k2_funct_2(c1_5__funct_7,c2_5__funct_7,c3_5__funct_7,A),B))
               => r2_hidden(k1_funct_1(k2_funct_1(c3_5__funct_7),c4_5__funct_7),k6_subset_1(c1_5__funct_7,A,k3_funct_2(c1_5__funct_7,c2_5__funct_7,c3_5__funct_7,B))) ) ) ) )
   => ! [C] : 
        ( m1_subset_1(C,c2_5__funct_7)
       => ! [D] : 
            ( m1_subset_1(D,k1_zfmisc_1(c1_5__funct_7))
           => ! [E] : 
                ( m1_subset_1(E,k1_zfmisc_1(c2_5__funct_7))
               => ( r2_hidden(C,k6_subset_1(c2_5__funct_7,k2_funct_2(c1_5__funct_7,c2_5__funct_7,c3_5__funct_7,D),E))
                 => r2_hidden(k1_funct_1(k2_funct_1(c3_5__funct_7),C),k6_subset_1(c1_5__funct_7,D,k3_funct_2(c1_5__funct_7,c2_5__funct_7,c3_5__funct_7,E))) ) ) ) ) ),
    introduced(definition,[new_symbol(c4_5__funct_7),file(funct_7,c4_5__funct_7)]),
    [interesting(0.8),axiom,file(funct_7,c4_5__funct_7)]).

fof(dh_c5_5__funct_7,definition,
    ( ( m1_subset_1(c5_5__funct_7,k1_zfmisc_1(c1_5__funct_7))
     => ! [A] : 
          ( m1_subset_1(A,k1_zfmisc_1(c2_5__funct_7))
         => ( r2_hidden(c4_5__funct_7,k6_subset_1(c2_5__funct_7,k2_funct_2(c1_5__funct_7,c2_5__funct_7,c3_5__funct_7,c5_5__funct_7),A))
           => r2_hidden(k1_funct_1(k2_funct_1(c3_5__funct_7),c4_5__funct_7),k6_subset_1(c1_5__funct_7,c5_5__funct_7,k3_funct_2(c1_5__funct_7,c2_5__funct_7,c3_5__funct_7,A))) ) ) )
   => ! [B] : 
        ( m1_subset_1(B,k1_zfmisc_1(c1_5__funct_7))
       => ! [C] : 
            ( m1_subset_1(C,k1_zfmisc_1(c2_5__funct_7))
           => ( r2_hidden(c4_5__funct_7,k6_subset_1(c2_5__funct_7,k2_funct_2(c1_5__funct_7,c2_5__funct_7,c3_5__funct_7,B),C))
             => r2_hidden(k1_funct_1(k2_funct_1(c3_5__funct_7),c4_5__funct_7),k6_subset_1(c1_5__funct_7,B,k3_funct_2(c1_5__funct_7,c2_5__funct_7,c3_5__funct_7,C))) ) ) ) ),
    introduced(definition,[new_symbol(c5_5__funct_7),file(funct_7,c5_5__funct_7)]),
    [interesting(0.8),axiom,file(funct_7,c5_5__funct_7)]).

fof(dh_c6_5__funct_7,definition,
    ( ( m1_subset_1(c6_5__funct_7,k1_zfmisc_1(c2_5__funct_7))
     => ( r2_hidden(c4_5__funct_7,k6_subset_1(c2_5__funct_7,k2_funct_2(c1_5__funct_7,c2_5__funct_7,c3_5__funct_7,c5_5__funct_7),c6_5__funct_7))
       => r2_hidden(k1_funct_1(k2_funct_1(c3_5__funct_7),c4_5__funct_7),k6_subset_1(c1_5__funct_7,c5_5__funct_7,k3_funct_2(c1_5__funct_7,c2_5__funct_7,c3_5__funct_7,c6_5__funct_7))) ) )
   => ! [A] : 
        ( m1_subset_1(A,k1_zfmisc_1(c2_5__funct_7))
       => ( r2_hidden(c4_5__funct_7,k6_subset_1(c2_5__funct_7,k2_funct_2(c1_5__funct_7,c2_5__funct_7,c3_5__funct_7,c5_5__funct_7),A))
         => r2_hidden(k1_funct_1(k2_funct_1(c3_5__funct_7),c4_5__funct_7),k6_subset_1(c1_5__funct_7,c5_5__funct_7,k3_funct_2(c1_5__funct_7,c2_5__funct_7,c3_5__funct_7,A))) ) ) ),
    introduced(definition,[new_symbol(c6_5__funct_7),file(funct_7,c6_5__funct_7)]),
    [interesting(0.8),axiom,file(funct_7,c6_5__funct_7)]).

fof(e2_5__funct_7,assumption,(
    r2_hidden(c4_5__funct_7,k6_subset_1(c2_5__funct_7,k2_funct_2(c1_5__funct_7,c2_5__funct_7,c3_5__funct_7,c5_5__funct_7),c6_5__funct_7)) ),
    introduced(assumption,[file(funct_7,e2_5__funct_7)]),
    [interesting(0.8),axiom,file(funct_7,e2_5__funct_7)]).

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(fc18_finseq_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finset_1(A) )
     => v1_finset_1(k10_relat_1(A,B)) ) ),
    file(finseq_1,fc18_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,fc18_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(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(dt_k10_relat_1,axiom,(
    $true ),
    file(relat_1,k10_relat_1),
    [interesting(0.9),axiom,file(relat_1,k10_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_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k2_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,k2_zfmisc_1)]).

fof(dt_k4_xboole_0,axiom,(
    $true ),
    file(xboole_0,k4_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k4_xboole_0)]).

fof(dt_k9_relat_1,axiom,(
    $true ),
    file(relat_1,k9_relat_1),
    [interesting(0.9),axiom,file(relat_1,k9_relat_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(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(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(fc3_relat_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_relat_1(B) )
     => v1_relat_1(k4_xboole_0(A,B)) ) ),
    file(relat_1,fc3_relat_1),
    [interesting(0.9),axiom,file(relat_1,fc3_relat_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(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_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(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(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(t3_boole,theorem,(
    ! [A] : k4_xboole_0(A,k1_xboole_0) = A ),
    file(boole,t3_boole),
    [interesting(0.9),axiom,file(boole,t3_boole)]).

fof(t4_boole,theorem,(
    ! [A] : k4_xboole_0(k1_xboole_0,A) = k1_xboole_0 ),
    file(boole,t4_boole),
    [interesting(0.9),axiom,file(boole,t4_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_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(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_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(redefinition_k3_funct_2,definition,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(C)
        & m1_relset_1(C,A,B) )
     => k3_funct_2(A,B,C,D) = k10_relat_1(C,D) ) ),
    file(funct_2,k3_funct_2),
    [interesting(0.9),axiom,file(funct_2,k3_funct_2)]).

fof(redefinition_k6_subset_1,definition,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k6_subset_1(A,B,C) = k4_xboole_0(B,C) ) ),
    file(subset_1,k6_subset_1),
    [interesting(0.9),axiom,file(subset_1,k6_subset_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_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k1_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,k1_zfmisc_1)]).

fof(dt_k2_funct_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(k2_funct_1(A))
        & v1_funct_1(k2_funct_1(A)) ) ) ),
    file(funct_1,k2_funct_1),
    [interesting(0.9),axiom,file(funct_1,k2_funct_1)]).

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(dt_k3_funct_2,axiom,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(C)
        & m1_relset_1(C,A,B) )
     => m1_subset_1(k3_funct_2(A,B,C,D),k1_zfmisc_1(A)) ) ),
    file(funct_2,k3_funct_2),
    [interesting(0.9),axiom,file(funct_2,k3_funct_2)]).

fof(dt_k6_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(k6_subset_1(A,B,C),k1_zfmisc_1(A)) ) ),
    file(subset_1,k6_subset_1),
    [interesting(0.9),axiom,file(subset_1,k6_subset_1)]).

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_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    [interesting(0.9),axiom,file(subset_1,m1_subset_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_5__funct_7,assumption,(
    ~ v1_xboole_0(c1_5__funct_7) ),
    introduced(assumption,[file(funct_7,c1_5__funct_7)]),
    [interesting(0.8),axiom,file(funct_7,c1_5__funct_7)]).

fof(dt_c2_5__funct_7,assumption,(
    ~ v1_xboole_0(c2_5__funct_7) ),
    introduced(assumption,[file(funct_7,c2_5__funct_7)]),
    [interesting(0.8),axiom,file(funct_7,c2_5__funct_7)]).

fof(dt_c3_5__funct_7,assumption,
    ( v1_funct_1(c3_5__funct_7)
    & v1_funct_2(c3_5__funct_7,c1_5__funct_7,c2_5__funct_7)
    & m2_relset_1(c3_5__funct_7,c1_5__funct_7,c2_5__funct_7) ),
    introduced(assumption,[file(funct_7,c3_5__funct_7)]),
    [interesting(0.8),axiom,file(funct_7,c3_5__funct_7)]).

fof(dt_c4_5__funct_7,assumption,(
    m1_subset_1(c4_5__funct_7,c2_5__funct_7) ),
    introduced(assumption,[file(funct_7,c4_5__funct_7)]),
    [interesting(0.8),axiom,file(funct_7,c4_5__funct_7)]).

fof(dt_c5_5__funct_7,assumption,(
    m1_subset_1(c5_5__funct_7,k1_zfmisc_1(c1_5__funct_7)) ),
    introduced(assumption,[file(funct_7,c5_5__funct_7)]),
    [interesting(0.8),axiom,file(funct_7,c5_5__funct_7)]).

fof(dt_c6_5__funct_7,assumption,(
    m1_subset_1(c6_5__funct_7,k1_zfmisc_1(c2_5__funct_7)) ),
    introduced(assumption,[file(funct_7,c6_5__funct_7)]),
    [interesting(0.8),axiom,file(funct_7,c6_5__funct_7)]).

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(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(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(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(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(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(t6_boole,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => A = k1_xboole_0 ) ),
    file(boole,t6_boole),
    [interesting(0.9),axiom,file(boole,t6_boole)]).

fof(t7_boole,theorem,(
    ! [A,B] : 
      ~ ( r2_hidden(A,B)
        & v1_xboole_0(B) ) ),
    file(boole,t7_boole),
    [interesting(0.9),axiom,file(boole,t7_boole)]).

fof(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(de_c7_5__funct_7,definition,(
    c7_5__funct_7 = k1_funct_1(k2_funct_1(c3_5__funct_7),c4_5__funct_7) ),
    introduced(definition,[new_symbol(c7_5__funct_7),file(funct_7,c7_5__funct_7)]),
    [interesting(0.8),axiom,file(funct_7,c7_5__funct_7)]).

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(dt_k1_relat_1,axiom,(
    $true ),
    file(relat_1,k1_relat_1),
    [interesting(0.9),axiom,file(relat_1,k1_relat_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(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(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(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(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(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(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(redefinition_k5_relset_1,definition,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => k5_relset_1(A,B,C) = k2_relat_1(C) ) ),
    file(relset_1,k5_relset_1),
    [interesting(0.9),axiom,file(relset_1,k5_relset_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_k5_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => m1_subset_1(k5_relset_1(A,B,C),k1_zfmisc_1(B)) ) ),
    file(relset_1,k5_relset_1),
    [interesting(0.9),axiom,file(relset_1,k5_relset_1)]).

fof(t144_relat_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => r1_tarski(k9_relat_1(B,A),k2_relat_1(B)) ) ),
    file(relat_1,t144_relat_1),
    [interesting(0.9),axiom,file(relat_1,t144_relat_1)]).

fof(e4_5__funct_7,plain,(
    r1_tarski(k2_funct_2(c1_5__funct_7,c2_5__funct_7,c3_5__funct_7,c5_5__funct_7),k5_relset_1(c1_5__funct_7,c2_5__funct_7,c3_5__funct_7)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5__funct_7,dt_c2_5__funct_7,dt_c3_5__funct_7,dt_c5_5__funct_7])],[cc1_finseq_1,fc11_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,dt_k2_zfmisc_1,cc1_relset_1,fc12_relat_1,fc2_finseq_1,fc4_relat_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,fc6_relat_1,fc8_relat_1,rc1_funct_1,rc1_relat_1,rc1_subset_1,rc2_funct_1,rc2_partfun1,rc2_relat_1,rc2_subset_1,t2_subset,t6_boole,t7_boole,t8_boole,reflexivity_r1_tarski,redefinition_k2_funct_2,redefinition_k5_relset_1,dt_k2_funct_2,dt_k2_relat_1,dt_k5_relset_1,dt_k9_relat_1,dt_c1_5__funct_7,dt_c2_5__funct_7,dt_c3_5__funct_7,dt_c5_5__funct_7,t3_subset,t144_relat_1]),
    [interesting(0.8),file(funct_7,e4_5__funct_7),[file(funct_7,e4_5__funct_7)]]).

fof(d4_xboole_0,definition,(
    ! [A,B,C] : 
      ( C = k4_xboole_0(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( r2_hidden(D,A)
            & ~ r2_hidden(D,B) ) ) ) ),
    file(xboole_0,d4_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,d4_xboole_0)]).

fof(e3_5__funct_7,plain,(
    r2_hidden(c4_5__funct_7,k2_funct_2(c1_5__funct_7,c2_5__funct_7,c3_5__funct_7,c5_5__funct_7)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5__funct_7,dt_c2_5__funct_7,dt_c3_5__funct_7,dt_c4_5__funct_7,dt_c5_5__funct_7,dt_c6_5__funct_7,e2_5__funct_7])],[cc1_finseq_1,rc1_finseq_1,rc1_partfun1,rc3_finseq_1,rc3_funct_1,rc3_relat_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,reflexivity_r1_tarski,dt_k1_xboole_0,dt_k2_zfmisc_1,cc1_relset_1,cc2_funct_1,fc12_relat_1,fc2_finseq_1,fc3_relat_1,fc4_relat_1,fc4_subset_1,rc1_funct_1,rc1_relat_1,rc2_funct_1,rc2_partfun1,rc2_relat_1,t3_boole,t4_boole,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_zfmisc_1,dt_k9_relat_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,cc1_funct_1,cc1_relat_1,fc1_subset_1,rc1_subset_1,rc2_subset_1,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,redefinition_k2_funct_2,redefinition_k6_subset_1,dt_k2_funct_2,dt_k4_xboole_0,dt_k6_subset_1,dt_c1_5__funct_7,dt_c2_5__funct_7,dt_c3_5__funct_7,dt_c4_5__funct_7,dt_c5_5__funct_7,dt_c6_5__funct_7,t1_subset,t7_boole,e2_5__funct_7,d4_xboole_0]),
    [interesting(0.8),file(funct_7,e3_5__funct_7),[file(funct_7,e3_5__funct_7)]]).

fof(t54_funct_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v2_funct_1(A)
       => ! [B] : 
            ( ( v1_relat_1(B)
              & v1_funct_1(B) )
           => ( B = k2_funct_1(A)
            <=> ( k1_relat_1(B) = k2_relat_1(A)
                & ! [C,D] : 
                    ( ( ( r2_hidden(C,k2_relat_1(A))
                        & D = k1_funct_1(B,C) )
                     => ( r2_hidden(D,k1_relat_1(A))
                        & C = k1_funct_1(A,D) ) )
                    & ( ( r2_hidden(D,k1_relat_1(A))
                        & C = k1_funct_1(A,D) )
                     => ( r2_hidden(C,k2_relat_1(A))
                        & D = k1_funct_1(B,C) ) ) ) ) ) ) ) ) ),
    file(funct_1,t54_funct_1),
    [interesting(0.9),axiom,file(funct_1,t54_funct_1)]).

fof(e5_5__funct_7,plain,(
    r2_hidden(k1_funct_1(k2_funct_1(c3_5__funct_7),c4_5__funct_7),k4_relset_1(c1_5__funct_7,c2_5__funct_7,c3_5__funct_7)) ),
    inference(mizar_by,[status(thm),assumptions([e1_5__funct_7,dt_c1_5__funct_7,dt_c2_5__funct_7,dt_c3_5__funct_7,dt_c4_5__funct_7,dt_c5_5__funct_7,dt_c6_5__funct_7,e2_5__funct_7])],[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,dt_k2_zfmisc_1,cc1_relset_1,fc12_relat_1,fc2_finseq_1,fc4_relat_1,fc4_subset_1,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_zfmisc_1,dt_k9_relat_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_partfun1,rc1_relat_1,rc1_subset_1,rc2_funct_1,rc2_partfun1,rc2_relat_1,rc2_subset_1,t2_subset,t4_subset,t5_subset,t6_boole,t8_boole,reflexivity_r1_tarski,antisymmetry_r2_hidden,redefinition_k2_funct_2,redefinition_k4_relset_1,redefinition_k5_relset_1,dt_k1_funct_1,dt_k1_relat_1,dt_k2_funct_1,dt_k2_funct_2,dt_k2_relat_1,dt_k4_relset_1,dt_k5_relset_1,dt_c1_5__funct_7,dt_c2_5__funct_7,dt_c3_5__funct_7,dt_c4_5__funct_7,dt_c5_5__funct_7,rc1_funct_1,rc3_funct_1,t1_subset,t3_subset,t7_boole,e4_5__funct_7,e1_5__funct_7,e3_5__funct_7,t54_funct_1]),
    [interesting(0.8),file(funct_7,e5_5__funct_7),[file(funct_7,e5_5__funct_7)]]).

fof(e6_5__funct_7,plain,(
    m1_subset_1(k1_funct_1(k2_funct_1(c3_5__funct_7),c4_5__funct_7),c1_5__funct_7) ),
    inference(mizar_by,[status(thm),assumptions([e1_5__funct_7,dt_c1_5__funct_7,dt_c2_5__funct_7,dt_c3_5__funct_7,dt_c4_5__funct_7,dt_c5_5__funct_7,dt_c6_5__funct_7,e2_5__funct_7])],[cc1_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,reflexivity_r1_tarski,dt_k1_xboole_0,dt_k2_zfmisc_1,cc1_relset_1,fc12_relat_1,fc2_finseq_1,fc4_relat_1,fc4_subset_1,rc1_partfun1,rc3_funct_1,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_relat_1,dt_k1_zfmisc_1,dt_m1_relset_1,dt_m2_relset_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc1_subset_1,fc5_relat_1,fc7_relat_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,redefinition_k4_relset_1,dt_k1_funct_1,dt_k2_funct_1,dt_k4_relset_1,dt_m1_subset_1,dt_c1_5__funct_7,dt_c2_5__funct_7,dt_c3_5__funct_7,dt_c4_5__funct_7,t1_subset,t7_boole,e5_5__funct_7]),
    [interesting(0.8),file(funct_7,e6_5__funct_7),[file(funct_7,e6_5__funct_7)]]).

fof(dt_c7_5__funct_7,plain,(
    m1_subset_1(c7_5__funct_7,c1_5__funct_7) ),
    inference(mizar_by,[status(thm),assumptions([e1_5__funct_7,dt_c1_5__funct_7,dt_c2_5__funct_7,dt_c3_5__funct_7,dt_c4_5__funct_7,dt_c5_5__funct_7,dt_c6_5__funct_7,e2_5__funct_7])],[reflexivity_r1_tarski,cc1_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,existence_m1_relset_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc12_relat_1,fc1_subset_1,fc2_finseq_1,fc4_relat_1,fc4_subset_1,rc1_partfun1,rc1_subset_1,rc2_partfun1,rc2_subset_1,rc3_funct_1,t1_subset,t3_subset,t4_subset,t5_subset,existence_m2_relset_1,redefinition_m2_relset_1,dt_m2_relset_1,dt_c2_5__funct_7,cc1_funct_1,cc1_relat_1,cc2_funct_1,rc1_funct_1,rc1_relat_1,rc2_funct_1,rc2_relat_1,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_subset_1,dt_k1_funct_1,dt_k2_funct_1,dt_m1_subset_1,dt_c1_5__funct_7,dt_c3_5__funct_7,dt_c4_5__funct_7,de_c7_5__funct_7,e6_5__funct_7]),
    [interesting(0.8),file(funct_7,c7_5__funct_7),[file(funct_7,c7_5__funct_7)]]).

fof(fc10_relat_1,theorem,(
    ! [A,B] : 
      ( ( v1_xboole_0(A)
        & v1_relat_1(B) )
     => ( v1_xboole_0(k5_relat_1(B,A))
        & v1_relat_1(k5_relat_1(B,A)) ) ) ),
    file(relat_1,fc10_relat_1),
    [interesting(0.9),axiom,file(relat_1,fc10_relat_1)]).

fof(fc9_relat_1,theorem,(
    ! [A,B] : 
      ( ( v1_xboole_0(A)
        & v1_relat_1(B) )
     => ( v1_xboole_0(k5_relat_1(A,B))
        & v1_relat_1(k5_relat_1(A,B)) ) ) ),
    file(relat_1,fc9_relat_1),
    [interesting(0.9),axiom,file(relat_1,fc9_relat_1)]).

fof(dt_k5_relat_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_relat_1(B) )
     => v1_relat_1(k5_relat_1(A,B)) ) ),
    file(relat_1,k5_relat_1),
    [interesting(0.9),axiom,file(relat_1,k5_relat_1)]).

fof(fc1_funct_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B) )
     => ( v1_relat_1(k5_relat_1(A,B))
        & v1_funct_1(k5_relat_1(A,B)) ) ) ),
    file(funct_1,fc1_funct_1),
    [interesting(0.9),axiom,file(funct_1,fc1_funct_1)]).

fof(t57_funct_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( ( v2_funct_1(B)
          & r2_hidden(A,k2_relat_1(B)) )
       => ( A = k1_funct_1(B,k1_funct_1(k2_funct_1(B),A))
          & A = k1_funct_1(k5_relat_1(k2_funct_1(B),B),A) ) ) ) ),
    file(funct_1,t57_funct_1),
    [interesting(0.9),axiom,file(funct_1,t57_funct_1)]).

fof(e7_5__funct_7,plain,(
    c4_5__funct_7 = k8_funct_2(c1_5__funct_7,c2_5__funct_7,c3_5__funct_7,c7_5__funct_7) ),
    inference(mizar_by,[status(thm),assumptions([e1_5__funct_7,dt_c4_5__funct_7,dt_c6_5__funct_7,e2_5__funct_7,dt_c1_5__funct_7,dt_c2_5__funct_7,dt_c3_5__funct_7,dt_c5_5__funct_7])],[cc1_finseq_1,fc11_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,dt_k2_zfmisc_1,cc1_relset_1,fc12_relat_1,fc2_finseq_1,fc4_relat_1,fc4_subset_1,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_zfmisc_1,dt_k9_relat_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc10_relat_1,fc1_subset_1,fc6_relat_1,fc8_relat_1,fc9_relat_1,rc1_partfun1,rc1_relat_1,rc1_subset_1,rc2_funct_1,rc2_partfun1,rc2_relat_1,rc2_subset_1,t2_subset,t4_subset,t5_subset,t6_boole,t8_boole,reflexivity_r1_tarski,antisymmetry_r2_hidden,redefinition_k2_funct_2,redefinition_k5_relset_1,redefinition_k8_funct_2,dt_k1_funct_1,dt_k2_funct_1,dt_k2_funct_2,dt_k2_relat_1,dt_k5_relat_1,dt_k5_relset_1,dt_k8_funct_2,dt_c1_5__funct_7,dt_c2_5__funct_7,dt_c3_5__funct_7,dt_c4_5__funct_7,dt_c5_5__funct_7,dt_c7_5__funct_7,de_c7_5__funct_7,fc1_funct_1,rc1_funct_1,rc3_funct_1,t1_subset,t3_subset,t7_boole,e1_5__funct_7,e3_5__funct_7,e4_5__funct_7,t57_funct_1]),
    [interesting(0.8),file(funct_7,e7_5__funct_7),[file(funct_7,e7_5__funct_7)]]).

fof(t4_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))
                       => ! [F] : 
                            ( m1_subset_1(F,k1_zfmisc_1(B))
                           => ( r2_hidden(k8_funct_2(A,B,C,D),k6_subset_1(B,k2_funct_2(A,B,C,E),F))
                             => r2_hidden(D,k6_subset_1(A,E,k3_funct_2(A,B,C,F))) ) ) ) ) ) ) ) ) ),
    file(funct_7,t4_funct_7),
    [interesting(0.9),axiom,file(funct_7,t4_funct_7)]).

fof(e8_5__funct_7,plain,(
    r2_hidden(k1_funct_1(k2_funct_1(c3_5__funct_7),c4_5__funct_7),k6_subset_1(c1_5__funct_7,c5_5__funct_7,k3_funct_2(c1_5__funct_7,c2_5__funct_7,c3_5__funct_7,c6_5__funct_7))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c4_5__funct_7,dt_c6_5__funct_7,dt_c1_5__funct_7,dt_c2_5__funct_7,dt_c3_5__funct_7,dt_c5_5__funct_7,e1_5__funct_7,e2_5__funct_7])],[cc1_finseq_1,fc18_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,existence_m1_relset_1,dt_k10_relat_1,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_k4_xboole_0,dt_k9_relat_1,dt_m1_relset_1,cc1_relset_1,cc2_funct_1,fc12_relat_1,fc2_finseq_1,fc3_relat_1,fc4_relat_1,fc4_subset_1,rc1_funct_1,rc1_partfun1,rc1_relat_1,rc2_funct_1,rc2_partfun1,rc2_relat_1,rc3_funct_1,t3_boole,t4_boole,antisymmetry_r2_hidden,existence_m1_subset_1,existence_m2_relset_1,redefinition_k2_funct_2,redefinition_k3_funct_2,redefinition_k6_subset_1,redefinition_k8_funct_2,redefinition_m2_relset_1,dt_k1_funct_1,dt_k1_zfmisc_1,dt_k2_funct_1,dt_k2_funct_2,dt_k3_funct_2,dt_k6_subset_1,dt_k8_funct_2,dt_m1_subset_1,dt_m2_relset_1,dt_c1_5__funct_7,dt_c2_5__funct_7,dt_c3_5__funct_7,dt_c4_5__funct_7,dt_c5_5__funct_7,dt_c6_5__funct_7,dt_c7_5__funct_7,de_c7_5__funct_7,cc1_funct_1,cc1_relat_1,fc1_subset_1,rc1_subset_1,rc2_subset_1,t1_subset,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole,e7_5__funct_7,e1_5__funct_7,e2_5__funct_7,t4_funct_7]),
    [interesting(0.8),file(funct_7,e8_5__funct_7),[file(funct_7,e8_5__funct_7)]]).

fof(i8_5__funct_7,theorem,(
    $true ),
    introduced(tautology,[file(funct_7,i8_5__funct_7)]),
    [interesting(0.8),trivial,file(funct_7,i8_5__funct_7)]).

fof(i7_5__funct_7,plain,(
    r2_hidden(k1_funct_1(k2_funct_1(c3_5__funct_7),c4_5__funct_7),k6_subset_1(c1_5__funct_7,c5_5__funct_7,k3_funct_2(c1_5__funct_7,c2_5__funct_7,c3_5__funct_7,c6_5__funct_7))) ),
    inference(conclusion,[status(thm),assumptions([dt_c4_5__funct_7,dt_c6_5__funct_7,dt_c1_5__funct_7,dt_c2_5__funct_7,dt_c3_5__funct_7,dt_c5_5__funct_7,e1_5__funct_7,e2_5__funct_7])],[e8_5__funct_7,i8_5__funct_7]),
    [interesting(0.8),file(funct_7,i7_5__funct_7),[file(funct_7,i7_5__funct_7)]]).

fof(i6_5__funct_7,plain,
    ( r2_hidden(c4_5__funct_7,k6_subset_1(c2_5__funct_7,k2_funct_2(c1_5__funct_7,c2_5__funct_7,c3_5__funct_7,c5_5__funct_7),c6_5__funct_7))
   => r2_hidden(k1_funct_1(k2_funct_1(c3_5__funct_7),c4_5__funct_7),k6_subset_1(c1_5__funct_7,c5_5__funct_7,k3_funct_2(c1_5__funct_7,c2_5__funct_7,c3_5__funct_7,c6_5__funct_7))) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c4_5__funct_7,dt_c6_5__funct_7,dt_c1_5__funct_7,dt_c2_5__funct_7,dt_c3_5__funct_7,dt_c5_5__funct_7,e1_5__funct_7]),discharge_asm(discharge,[e2_5__funct_7])],[e2_5__funct_7,i7_5__funct_7]),
    [interesting(0.8),file(funct_7,i6_5__funct_7),[file(funct_7,i6_5__funct_7)]]).

fof(i6_5_tmp__funct_7,plain,
    ( m1_subset_1(c6_5__funct_7,k1_zfmisc_1(c2_5__funct_7))
   => ( r2_hidden(c4_5__funct_7,k6_subset_1(c2_5__funct_7,k2_funct_2(c1_5__funct_7,c2_5__funct_7,c3_5__funct_7,c5_5__funct_7),c6_5__funct_7))
     => r2_hidden(k1_funct_1(k2_funct_1(c3_5__funct_7),c4_5__funct_7),k6_subset_1(c1_5__funct_7,c5_5__funct_7,k3_funct_2(c1_5__funct_7,c2_5__funct_7,c3_5__funct_7,c6_5__funct_7))) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c4_5__funct_7,dt_c1_5__funct_7,dt_c2_5__funct_7,dt_c3_5__funct_7,dt_c5_5__funct_7,e1_5__funct_7]),discharge_asm(discharge,[dt_c6_5__funct_7])],[dt_c6_5__funct_7,i6_5__funct_7]),
    [interesting(0.8),i5_5__funct_7]).

fof(i5_5__funct_7,plain,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(c2_5__funct_7))
     => ( r2_hidden(c4_5__funct_7,k6_subset_1(c2_5__funct_7,k2_funct_2(c1_5__funct_7,c2_5__funct_7,c3_5__funct_7,c5_5__funct_7),A))
       => r2_hidden(k1_funct_1(k2_funct_1(c3_5__funct_7),c4_5__funct_7),k6_subset_1(c1_5__funct_7,c5_5__funct_7,k3_funct_2(c1_5__funct_7,c2_5__funct_7,c3_5__funct_7,A))) ) ) ),
    inference(let,[status(thm),assumptions([dt_c4_5__funct_7,dt_c1_5__funct_7,dt_c2_5__funct_7,dt_c3_5__funct_7,dt_c5_5__funct_7,e1_5__funct_7])],[i6_5_tmp__funct_7,dh_c6_5__funct_7]),
    [interesting(0.8),file(funct_7,i5_5__funct_7),[file(funct_7,i5_5__funct_7)]]).

fof(i5_5_tmp__funct_7,plain,
    ( m1_subset_1(c5_5__funct_7,k1_zfmisc_1(c1_5__funct_7))
   => ! [A] : 
        ( m1_subset_1(A,k1_zfmisc_1(c2_5__funct_7))
       => ( r2_hidden(c4_5__funct_7,k6_subset_1(c2_5__funct_7,k2_funct_2(c1_5__funct_7,c2_5__funct_7,c3_5__funct_7,c5_5__funct_7),A))
         => r2_hidden(k1_funct_1(k2_funct_1(c3_5__funct_7),c4_5__funct_7),k6_subset_1(c1_5__funct_7,c5_5__funct_7,k3_funct_2(c1_5__funct_7,c2_5__funct_7,c3_5__funct_7,A))) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c4_5__funct_7,dt_c1_5__funct_7,dt_c2_5__funct_7,dt_c3_5__funct_7,e1_5__funct_7]),discharge_asm(discharge,[dt_c5_5__funct_7])],[dt_c5_5__funct_7,i5_5__funct_7]),
    [interesting(0.8),i4_5__funct_7]).

fof(i4_5__funct_7,plain,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(c1_5__funct_7))
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(c2_5__funct_7))
         => ( r2_hidden(c4_5__funct_7,k6_subset_1(c2_5__funct_7,k2_funct_2(c1_5__funct_7,c2_5__funct_7,c3_5__funct_7,A),B))
           => r2_hidden(k1_funct_1(k2_funct_1(c3_5__funct_7),c4_5__funct_7),k6_subset_1(c1_5__funct_7,A,k3_funct_2(c1_5__funct_7,c2_5__funct_7,c3_5__funct_7,B))) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c4_5__funct_7,dt_c1_5__funct_7,dt_c2_5__funct_7,dt_c3_5__funct_7,e1_5__funct_7])],[i5_5_tmp__funct_7,dh_c5_5__funct_7]),
    [interesting(0.8),file(funct_7,i4_5__funct_7),[file(funct_7,i4_5__funct_7)]]).

fof(i4_5_tmp__funct_7,plain,
    ( m1_subset_1(c4_5__funct_7,c2_5__funct_7)
   => ! [A] : 
        ( m1_subset_1(A,k1_zfmisc_1(c1_5__funct_7))
       => ! [B] : 
            ( m1_subset_1(B,k1_zfmisc_1(c2_5__funct_7))
           => ( r2_hidden(c4_5__funct_7,k6_subset_1(c2_5__funct_7,k2_funct_2(c1_5__funct_7,c2_5__funct_7,c3_5__funct_7,A),B))
             => r2_hidden(k1_funct_1(k2_funct_1(c3_5__funct_7),c4_5__funct_7),k6_subset_1(c1_5__funct_7,A,k3_funct_2(c1_5__funct_7,c2_5__funct_7,c3_5__funct_7,B))) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_5__funct_7,dt_c2_5__funct_7,dt_c3_5__funct_7,e1_5__funct_7]),discharge_asm(discharge,[dt_c4_5__funct_7])],[dt_c4_5__funct_7,i4_5__funct_7]),
    [interesting(0.8),i3_5__funct_7]).

fof(i3_5__funct_7,plain,(
    ! [A] : 
      ( m1_subset_1(A,c2_5__funct_7)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(c1_5__funct_7))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(c2_5__funct_7))
             => ( r2_hidden(A,k6_subset_1(c2_5__funct_7,k2_funct_2(c1_5__funct_7,c2_5__funct_7,c3_5__funct_7,B),C))
               => r2_hidden(k1_funct_1(k2_funct_1(c3_5__funct_7),A),k6_subset_1(c1_5__funct_7,B,k3_funct_2(c1_5__funct_7,c2_5__funct_7,c3_5__funct_7,C))) ) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_5__funct_7,dt_c2_5__funct_7,dt_c3_5__funct_7,e1_5__funct_7])],[i4_5_tmp__funct_7,dh_c4_5__funct_7]),
    [interesting(0.8),file(funct_7,i3_5__funct_7),[file(funct_7,i3_5__funct_7)]]).

fof(i2_5__funct_7,plain,
    ( v2_funct_1(c3_5__funct_7)
   => ! [A] : 
        ( m1_subset_1(A,c2_5__funct_7)
       => ! [B] : 
            ( m1_subset_1(B,k1_zfmisc_1(c1_5__funct_7))
           => ! [C] : 
                ( m1_subset_1(C,k1_zfmisc_1(c2_5__funct_7))
               => ( r2_hidden(A,k6_subset_1(c2_5__funct_7,k2_funct_2(c1_5__funct_7,c2_5__funct_7,c3_5__funct_7,B),C))
                 => r2_hidden(k1_funct_1(k2_funct_1(c3_5__funct_7),A),k6_subset_1(c1_5__funct_7,B,k3_funct_2(c1_5__funct_7,c2_5__funct_7,c3_5__funct_7,C))) ) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_5__funct_7,dt_c2_5__funct_7,dt_c3_5__funct_7]),discharge_asm(discharge,[e1_5__funct_7])],[e1_5__funct_7,i3_5__funct_7]),
    [interesting(0.8),file(funct_7,i2_5__funct_7),[file(funct_7,i2_5__funct_7)]]).

fof(i2_5_tmp__funct_7,plain,
    ( ( v1_funct_1(c3_5__funct_7)
      & v1_funct_2(c3_5__funct_7,c1_5__funct_7,c2_5__funct_7)
      & m2_relset_1(c3_5__funct_7,c1_5__funct_7,c2_5__funct_7) )
   => ( v2_funct_1(c3_5__funct_7)
     => ! [A] : 
          ( m1_subset_1(A,c2_5__funct_7)
         => ! [B] : 
              ( m1_subset_1(B,k1_zfmisc_1(c1_5__funct_7))
             => ! [C] : 
                  ( m1_subset_1(C,k1_zfmisc_1(c2_5__funct_7))
                 => ( r2_hidden(A,k6_subset_1(c2_5__funct_7,k2_funct_2(c1_5__funct_7,c2_5__funct_7,c3_5__funct_7,B),C))
                   => r2_hidden(k1_funct_1(k2_funct_1(c3_5__funct_7),A),k6_subset_1(c1_5__funct_7,B,k3_funct_2(c1_5__funct_7,c2_5__funct_7,c3_5__funct_7,C))) ) ) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_5__funct_7,dt_c2_5__funct_7]),discharge_asm(discharge,[dt_c3_5__funct_7])],[dt_c3_5__funct_7,i2_5__funct_7]),
    [interesting(0.8),i1_5__funct_7]).

fof(i1_5__funct_7,plain,(
    ! [A] : 
      ( ( v1_funct_1(A)
        & v1_funct_2(A,c1_5__funct_7,c2_5__funct_7)
        & m2_relset_1(A,c1_5__funct_7,c2_5__funct_7) )
     => ( v2_funct_1(A)
       => ! [B] : 
            ( m1_subset_1(B,c2_5__funct_7)
           => ! [C] : 
                ( m1_subset_1(C,k1_zfmisc_1(c1_5__funct_7))
               => ! [D] : 
                    ( m1_subset_1(D,k1_zfmisc_1(c2_5__funct_7))
                   => ( r2_hidden(B,k6_subset_1(c2_5__funct_7,k2_funct_2(c1_5__funct_7,c2_5__funct_7,A,C),D))
                     => r2_hidden(k1_funct_1(k2_funct_1(A),B),k6_subset_1(c1_5__funct_7,C,k3_funct_2(c1_5__funct_7,c2_5__funct_7,A,D))) ) ) ) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_5__funct_7,dt_c2_5__funct_7])],[i2_5_tmp__funct_7,dh_c3_5__funct_7]),
    [interesting(0.8),file(funct_7,i1_5__funct_7),[file(funct_7,i1_5__funct_7)]]).

fof(i1_5_tmp__funct_7,plain,
    ( ( ~ v1_xboole_0(c1_5__funct_7)
      & ~ v1_xboole_0(c2_5__funct_7) )
   => ! [A] : 
        ( ( v1_funct_1(A)
          & v1_funct_2(A,c1_5__funct_7,c2_5__funct_7)
          & m2_relset_1(A,c1_5__funct_7,c2_5__funct_7) )
       => ( v2_funct_1(A)
         => ! [B] : 
              ( m1_subset_1(B,c2_5__funct_7)
             => ! [C] : 
                  ( m1_subset_1(C,k1_zfmisc_1(c1_5__funct_7))
                 => ! [D] : 
                      ( m1_subset_1(D,k1_zfmisc_1(c2_5__funct_7))
                     => ( r2_hidden(B,k6_subset_1(c2_5__funct_7,k2_funct_2(c1_5__funct_7,c2_5__funct_7,A,C),D))
                       => r2_hidden(k1_funct_1(k2_funct_1(A),B),k6_subset_1(c1_5__funct_7,C,k3_funct_2(c1_5__funct_7,c2_5__funct_7,A,D))) ) ) ) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_5__funct_7,dt_c2_5__funct_7])],[dt_c1_5__funct_7,dt_c2_5__funct_7,i1_5__funct_7]),
    [interesting(1),t5_funct_7]).

fof(t5_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,B)
                   => ! [E] : 
                        ( m1_subset_1(E,k1_zfmisc_1(A))
                       => ! [F] : 
                            ( m1_subset_1(F,k1_zfmisc_1(B))
                           => ( r2_hidden(D,k6_subset_1(B,k2_funct_2(A,B,C,E),F))
                             => r2_hidden(k1_funct_1(k2_funct_1(C),D),k6_subset_1(A,E,k3_funct_2(A,B,C,F))) ) ) ) ) ) ) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_5_tmp__funct_7,dh_c1_5__funct_7,dh_c2_5__funct_7]),
    [interesting(1),file(funct_7,t5_funct_7),[file(funct_7,t5_funct_7)]]).