% Mizar ND problem: t4_altcat_2,altcat_2,167,33 
fof(dh_c1_6__altcat_2,definition,
    ( ! [A] : 
        ( m1_pboole(A,c1_6__altcat_2)
       => ! [B] : 
            ( m1_pboole(B,c1_6__altcat_2)
           => ! [C] : 
                ( m1_pboole(C,c1_6__altcat_2)
               => ( r1_pzfmisc1(c1_6__altcat_2,A,B)
                 => ! [D] : 
                      ( m3_pboole(D,c1_6__altcat_2,A,B)
                     => ! [E] : 
                          ( m3_pboole(E,c1_6__altcat_2,B,C)
                         => m3_pboole(k13_pboole(D,E),c1_6__altcat_2,A,C) ) ) ) ) ) )
   => ! [F,G] : 
        ( m1_pboole(G,F)
       => ! [H] : 
            ( m1_pboole(H,F)
           => ! [I] : 
                ( m1_pboole(I,F)
               => ( r1_pzfmisc1(F,G,H)
                 => ! [J] : 
                      ( m3_pboole(J,F,G,H)
                     => ! [K] : 
                          ( m3_pboole(K,F,H,I)
                         => m3_pboole(k13_pboole(J,K),F,G,I) ) ) ) ) ) ) ),
    introduced(definition,[new_symbol(c1_6__altcat_2),file(altcat_2,c1_6__altcat_2)]),
    [interesting(0.8),axiom,file(altcat_2,c1_6__altcat_2)]).

fof(dh_c2_6__altcat_2,definition,
    ( ( m1_pboole(c2_6__altcat_2,c1_6__altcat_2)
     => ! [A] : 
          ( m1_pboole(A,c1_6__altcat_2)
         => ! [B] : 
              ( m1_pboole(B,c1_6__altcat_2)
             => ( r1_pzfmisc1(c1_6__altcat_2,c2_6__altcat_2,A)
               => ! [C] : 
                    ( m3_pboole(C,c1_6__altcat_2,c2_6__altcat_2,A)
                   => ! [D] : 
                        ( m3_pboole(D,c1_6__altcat_2,A,B)
                       => m3_pboole(k13_pboole(C,D),c1_6__altcat_2,c2_6__altcat_2,B) ) ) ) ) ) )
   => ! [E] : 
        ( m1_pboole(E,c1_6__altcat_2)
       => ! [F] : 
            ( m1_pboole(F,c1_6__altcat_2)
           => ! [G] : 
                ( m1_pboole(G,c1_6__altcat_2)
               => ( r1_pzfmisc1(c1_6__altcat_2,E,F)
                 => ! [H] : 
                      ( m3_pboole(H,c1_6__altcat_2,E,F)
                     => ! [I] : 
                          ( m3_pboole(I,c1_6__altcat_2,F,G)
                         => m3_pboole(k13_pboole(H,I),c1_6__altcat_2,E,G) ) ) ) ) ) ) ),
    introduced(definition,[new_symbol(c2_6__altcat_2),file(altcat_2,c2_6__altcat_2)]),
    [interesting(0.8),axiom,file(altcat_2,c2_6__altcat_2)]).

fof(dh_c3_6__altcat_2,definition,
    ( ( m1_pboole(c3_6__altcat_2,c1_6__altcat_2)
     => ! [A] : 
          ( m1_pboole(A,c1_6__altcat_2)
         => ( r1_pzfmisc1(c1_6__altcat_2,c2_6__altcat_2,c3_6__altcat_2)
           => ! [B] : 
                ( m3_pboole(B,c1_6__altcat_2,c2_6__altcat_2,c3_6__altcat_2)
               => ! [C] : 
                    ( m3_pboole(C,c1_6__altcat_2,c3_6__altcat_2,A)
                   => m3_pboole(k13_pboole(B,C),c1_6__altcat_2,c2_6__altcat_2,A) ) ) ) ) )
   => ! [D] : 
        ( m1_pboole(D,c1_6__altcat_2)
       => ! [E] : 
            ( m1_pboole(E,c1_6__altcat_2)
           => ( r1_pzfmisc1(c1_6__altcat_2,c2_6__altcat_2,D)
             => ! [F] : 
                  ( m3_pboole(F,c1_6__altcat_2,c2_6__altcat_2,D)
                 => ! [G] : 
                      ( m3_pboole(G,c1_6__altcat_2,D,E)
                     => m3_pboole(k13_pboole(F,G),c1_6__altcat_2,c2_6__altcat_2,E) ) ) ) ) ) ),
    introduced(definition,[new_symbol(c3_6__altcat_2),file(altcat_2,c3_6__altcat_2)]),
    [interesting(0.8),axiom,file(altcat_2,c3_6__altcat_2)]).

fof(dh_c4_6__altcat_2,definition,
    ( ( m1_pboole(c4_6__altcat_2,c1_6__altcat_2)
     => ( r1_pzfmisc1(c1_6__altcat_2,c2_6__altcat_2,c3_6__altcat_2)
       => ! [A] : 
            ( m3_pboole(A,c1_6__altcat_2,c2_6__altcat_2,c3_6__altcat_2)
           => ! [B] : 
                ( m3_pboole(B,c1_6__altcat_2,c3_6__altcat_2,c4_6__altcat_2)
               => m3_pboole(k13_pboole(A,B),c1_6__altcat_2,c2_6__altcat_2,c4_6__altcat_2) ) ) ) )
   => ! [C] : 
        ( m1_pboole(C,c1_6__altcat_2)
       => ( r1_pzfmisc1(c1_6__altcat_2,c2_6__altcat_2,c3_6__altcat_2)
         => ! [D] : 
              ( m3_pboole(D,c1_6__altcat_2,c2_6__altcat_2,c3_6__altcat_2)
             => ! [E] : 
                  ( m3_pboole(E,c1_6__altcat_2,c3_6__altcat_2,C)
                 => m3_pboole(k13_pboole(D,E),c1_6__altcat_2,c2_6__altcat_2,C) ) ) ) ) ),
    introduced(definition,[new_symbol(c4_6__altcat_2),file(altcat_2,c4_6__altcat_2)]),
    [interesting(0.8),axiom,file(altcat_2,c4_6__altcat_2)]).

fof(e1_6__altcat_2,assumption,(
    r1_pzfmisc1(c1_6__altcat_2,c2_6__altcat_2,c3_6__altcat_2) ),
    introduced(assumption,[file(altcat_2,e1_6__altcat_2)]),
    [interesting(0.8),axiom,file(altcat_2,e1_6__altcat_2)]).

fof(dh_c5_6__altcat_2,definition,
    ( ( m3_pboole(c5_6__altcat_2,c1_6__altcat_2,c2_6__altcat_2,c3_6__altcat_2)
     => ! [A] : 
          ( m3_pboole(A,c1_6__altcat_2,c3_6__altcat_2,c4_6__altcat_2)
         => m3_pboole(k13_pboole(c5_6__altcat_2,A),c1_6__altcat_2,c2_6__altcat_2,c4_6__altcat_2) ) )
   => ! [B] : 
        ( m3_pboole(B,c1_6__altcat_2,c2_6__altcat_2,c3_6__altcat_2)
       => ! [C] : 
            ( m3_pboole(C,c1_6__altcat_2,c3_6__altcat_2,c4_6__altcat_2)
           => m3_pboole(k13_pboole(B,C),c1_6__altcat_2,c2_6__altcat_2,c4_6__altcat_2) ) ) ),
    introduced(definition,[new_symbol(c5_6__altcat_2),file(altcat_2,c5_6__altcat_2)]),
    [interesting(0.8),axiom,file(altcat_2,c5_6__altcat_2)]).

fof(dh_c6_6__altcat_2,definition,
    ( ( m3_pboole(c6_6__altcat_2,c1_6__altcat_2,c3_6__altcat_2,c4_6__altcat_2)
     => m3_pboole(k13_pboole(c5_6__altcat_2,c6_6__altcat_2),c1_6__altcat_2,c2_6__altcat_2,c4_6__altcat_2) )
   => ! [A] : 
        ( m3_pboole(A,c1_6__altcat_2,c3_6__altcat_2,c4_6__altcat_2)
       => m3_pboole(k13_pboole(c5_6__altcat_2,A),c1_6__altcat_2,c2_6__altcat_2,c4_6__altcat_2) ) ),
    introduced(definition,[new_symbol(c6_6__altcat_2),file(altcat_2,c6_6__altcat_2)]),
    [interesting(0.8),axiom,file(altcat_2,c6_6__altcat_2)]).

fof(existence_m1_pboole,axiom,(
    ! [A] : 
    ? [B] : m1_pboole(B,A) ),
    file(pboole,m1_pboole),
    [interesting(0.9),axiom,file(pboole,m1_pboole)]).

fof(dt_m1_pboole,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ( v1_relat_1(B)
        & v1_funct_1(B) ) ) ),
    file(pboole,m1_pboole),
    [interesting(0.9),axiom,file(pboole,m1_pboole)]).

fof(dt_c3_6__altcat_2,assumption,(
    m1_pboole(c3_6__altcat_2,c1_6__altcat_2) ),
    introduced(assumption,[file(altcat_2,c3_6__altcat_2)]),
    [interesting(0.8),axiom,file(altcat_2,c3_6__altcat_2)]).

fof(cc3_pboole,theorem,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => ! [D] : 
          ( m3_pboole(D,A,B,C)
         => v1_funcop_1(D) ) ) ),
    file(pboole,cc3_pboole),
    [interesting(0.9),axiom,file(pboole,cc3_pboole)]).

fof(rc1_funcop_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v1_funcop_1(A) ) ),
    file(funcop_1,rc1_funcop_1),
    [interesting(0.9),axiom,file(funcop_1,rc1_funcop_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(rc4_pboole,theorem,(
    ! [A] : 
    ? [B] : 
      ( m1_pboole(B,A)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v1_funcop_1(B) ) ),
    file(pboole,rc4_pboole),
    [interesting(0.9),axiom,file(pboole,rc4_pboole)]).

fof(existence_m3_pboole,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => ? [D] : m3_pboole(D,A,B,C) ) ),
    file(pboole,m3_pboole),
    [interesting(0.9),axiom,file(pboole,m3_pboole)]).

fof(dt_k13_pboole,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_funcop_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & v1_funcop_1(B) )
     => ( v1_relat_1(k13_pboole(A,B))
        & v1_funct_1(k13_pboole(A,B))
        & v1_funcop_1(k13_pboole(A,B)) ) ) ),
    file(pboole,k13_pboole),
    [interesting(0.9),axiom,file(pboole,k13_pboole)]).

fof(dt_m3_pboole,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => ! [D] : 
          ( m3_pboole(D,A,B,C)
         => m1_pboole(D,A) ) ) ),
    file(pboole,m3_pboole),
    [interesting(0.9),axiom,file(pboole,m3_pboole)]).

fof(dt_c1_6__altcat_2,assumption,(
    $true ),
    introduced(assumption,[file(altcat_2,c1_6__altcat_2)]),
    [interesting(0.8),axiom,file(altcat_2,c1_6__altcat_2)]).

fof(dt_c2_6__altcat_2,assumption,(
    m1_pboole(c2_6__altcat_2,c1_6__altcat_2) ),
    introduced(assumption,[file(altcat_2,c2_6__altcat_2)]),
    [interesting(0.8),axiom,file(altcat_2,c2_6__altcat_2)]).

fof(dt_c4_6__altcat_2,assumption,(
    m1_pboole(c4_6__altcat_2,c1_6__altcat_2) ),
    introduced(assumption,[file(altcat_2,c4_6__altcat_2)]),
    [interesting(0.8),axiom,file(altcat_2,c4_6__altcat_2)]).

fof(dt_c5_6__altcat_2,assumption,(
    m3_pboole(c5_6__altcat_2,c1_6__altcat_2,c2_6__altcat_2,c3_6__altcat_2) ),
    introduced(assumption,[file(altcat_2,c5_6__altcat_2)]),
    [interesting(0.8),axiom,file(altcat_2,c5_6__altcat_2)]).

fof(dt_c6_6__altcat_2,assumption,(
    m3_pboole(c6_6__altcat_2,c1_6__altcat_2,c3_6__altcat_2,c4_6__altcat_2) ),
    introduced(assumption,[file(altcat_2,c6_6__altcat_2)]),
    [interesting(0.8),axiom,file(altcat_2,c6_6__altcat_2)]).

fof(de_c7_6__altcat_2,definition,(
    c7_6__altcat_2 = k13_pboole(c5_6__altcat_2,c6_6__altcat_2) ),
    introduced(definition,[new_symbol(c7_6__altcat_2),file(altcat_2,c7_6__altcat_2)]),
    [interesting(0.8),axiom,file(altcat_2,c7_6__altcat_2)]).

fof(t15_mssubfam,theorem,(
    ! [A,B] : 
      ( ( v1_funcop_1(B)
        & m1_pboole(B,A) )
     => ! [C] : 
          ( ( v1_funcop_1(C)
            & m1_pboole(C,A) )
         => ( v1_funcop_1(k13_pboole(B,C))
            & m1_pboole(k13_pboole(B,C),A) ) ) ) ),
    file(mssubfam,t15_mssubfam),
    [interesting(0.9),axiom,file(mssubfam,t15_mssubfam)]).

fof(e2_6__altcat_2,plain,
    ( v1_funcop_1(k13_pboole(c5_6__altcat_2,c6_6__altcat_2))
    & m1_pboole(k13_pboole(c5_6__altcat_2,c6_6__altcat_2),c1_6__altcat_2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_6__altcat_2,dt_c3_6__altcat_2,dt_c4_6__altcat_2,dt_c1_6__altcat_2,dt_c5_6__altcat_2,dt_c6_6__altcat_2])],[existence_m3_pboole,dt_m3_pboole,dt_c2_6__altcat_2,dt_c3_6__altcat_2,dt_c4_6__altcat_2,cc3_pboole,rc1_funcop_1,rc1_funct_1,rc4_pboole,existence_m1_pboole,dt_k13_pboole,dt_m1_pboole,dt_c1_6__altcat_2,dt_c5_6__altcat_2,dt_c6_6__altcat_2,t15_mssubfam]),
    [interesting(0.8),file(altcat_2,e2_6__altcat_2),[file(altcat_2,e2_6__altcat_2)]]).

fof(dt_c7_6__altcat_2,plain,
    ( v1_funcop_1(c7_6__altcat_2)
    & m1_pboole(c7_6__altcat_2,c1_6__altcat_2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_6__altcat_2,dt_c3_6__altcat_2,dt_c4_6__altcat_2,dt_c1_6__altcat_2,dt_c5_6__altcat_2,dt_c6_6__altcat_2])],[existence_m3_pboole,dt_m3_pboole,dt_c2_6__altcat_2,dt_c3_6__altcat_2,dt_c4_6__altcat_2,cc3_pboole,rc1_funcop_1,rc1_funct_1,rc4_pboole,existence_m1_pboole,dt_k13_pboole,dt_m1_pboole,dt_c1_6__altcat_2,dt_c5_6__altcat_2,dt_c6_6__altcat_2,de_c7_6__altcat_2,e2_6__altcat_2]),
    [interesting(0.8),file(altcat_2,c7_6__altcat_2),[file(altcat_2,c7_6__altcat_2)]]).

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(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(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_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(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_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(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(fc7_funcop_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_funcop_1(A) )
     => ( v1_relat_1(k1_funct_1(A,B))
        & v1_funct_1(k1_funct_1(A,B)) ) ) ),
    file(funcop_1,fc7_funcop_1),
    [interesting(0.9),axiom,file(funcop_1,fc7_funcop_1)]).

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(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_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_6_1__altcat_2,assumption,(
    $true ),
    introduced(assumption,[file(altcat_2,c1_6_1__altcat_2)]),
    [interesting(0.65),axiom,file(altcat_2,c1_6_1__altcat_2)]).

fof(d18_pboole,definition,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m1_pboole(D,A)
             => ( m3_pboole(D,A,B,C)
              <=> ! [E] : 
                    ( r2_hidden(E,A)
                   => ( v1_funct_1(k1_funct_1(D,E))
                      & v1_funct_2(k1_funct_1(D,E),k1_funct_1(B,E),k1_funct_1(C,E))
                      & m2_relset_1(k1_funct_1(D,E),k1_funct_1(B,E),k1_funct_1(C,E)) ) ) ) ) ) ) ),
    file(pboole,d18_pboole),
    [interesting(0.9),axiom,file(pboole,d18_pboole)]).

fof(dh_c1_6_1__altcat_2,definition,
    ( ~ ( r2_hidden(c1_6_1__altcat_2,c1_6__altcat_2)
        & ~ ( v1_funct_1(k1_funct_1(c7_6__altcat_2,c1_6_1__altcat_2))
            & v1_funct_2(k1_funct_1(c7_6__altcat_2,c1_6_1__altcat_2),k1_funct_1(c2_6__altcat_2,c1_6_1__altcat_2),k1_funct_1(c4_6__altcat_2,c1_6_1__altcat_2))
            & m2_relset_1(k1_funct_1(c7_6__altcat_2,c1_6_1__altcat_2),k1_funct_1(c2_6__altcat_2,c1_6_1__altcat_2),k1_funct_1(c4_6__altcat_2,c1_6_1__altcat_2)) ) )
   => ! [A] : 
        ~ ( r2_hidden(A,c1_6__altcat_2)
          & ~ ( v1_funct_1(k1_funct_1(c7_6__altcat_2,A))
              & v1_funct_2(k1_funct_1(c7_6__altcat_2,A),k1_funct_1(c2_6__altcat_2,A),k1_funct_1(c4_6__altcat_2,A))
              & m2_relset_1(k1_funct_1(c7_6__altcat_2,A),k1_funct_1(c2_6__altcat_2,A),k1_funct_1(c4_6__altcat_2,A)) ) ) ),
    introduced(definition,[new_symbol(c1_6_1__altcat_2),file(altcat_2,c1_6_1__altcat_2)]),
    [interesting(0.65),axiom,file(altcat_2,c1_6_1__altcat_2)]).

fof(e1_6_1__altcat_2,assumption,(
    r2_hidden(c1_6_1__altcat_2,c1_6__altcat_2) ),
    introduced(assumption,[file(altcat_2,e1_6_1__altcat_2)]),
    [interesting(0.65),axiom,file(altcat_2,e1_6_1__altcat_2)]).

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

fof(cc1_pboole,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_pboole(B,A)
         => ( v2_relat_1(B)
           => ~ v3_relat_1(B) ) ) ) ),
    file(pboole,cc1_pboole),
    [interesting(0.9),axiom,file(pboole,cc1_pboole)]).

fof(fc2_pboole,theorem,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v2_relat_1(B)
        & m1_pboole(B,A)
        & m1_subset_1(C,A) )
     => ~ v1_xboole_0(k1_funct_1(B,C)) ) ),
    file(pboole,fc2_pboole),
    [interesting(0.9),axiom,file(pboole,fc2_pboole)]).

fof(rc3_pboole,theorem,(
    ! [A] : 
    ? [B] : 
      ( m1_pboole(B,A)
      & v1_relat_1(B)
      & v2_relat_1(B)
      & v1_funct_1(B) ) ),
    file(pboole,rc3_pboole),
    [interesting(0.9),axiom,file(pboole,rc3_pboole)]).

fof(rc5_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v2_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc5_funct_1),
    [interesting(0.9),axiom,file(funct_1,rc5_funct_1)]).

fof(t1_subset,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => m1_subset_1(A,B) ) ),
    file(subset,t1_subset),
    [interesting(0.9),axiom,file(subset,t1_subset)]).

fof(t4_subset,theorem,(
    ! [A,B,C] : 
      ( ( r2_hidden(A,B)
        & m1_subset_1(B,k1_zfmisc_1(C)) )
     => m1_subset_1(A,C) ) ),
    file(subset,t4_subset),
    [interesting(0.9),axiom,file(subset,t4_subset)]).

fof(t5_subset,theorem,(
    ! [A,B,C] : 
      ~ ( r2_hidden(A,B)
        & m1_subset_1(B,k1_zfmisc_1(C))
        & v1_xboole_0(C) ) ),
    file(subset,t5_subset),
    [interesting(0.9),axiom,file(subset,t5_subset)]).

fof(existence_m1_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m1_relset_1(C,A,B) ),
    file(relset_1,m1_relset_1),
    [interesting(0.9),axiom,file(relset_1,m1_relset_1)]).

fof(existence_m1_subset_1,axiom,(
    ! [A] : 
    ? [B] : m1_subset_1(B,A) ),
    file(subset_1,m1_subset_1),
    [interesting(0.9),axiom,file(subset_1,m1_subset_1)]).

fof(cc2_pboole,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_pboole(B,A)
         => ( v3_relat_1(B)
           => ~ v2_relat_1(B) ) ) ) ),
    file(pboole,cc2_pboole),
    [interesting(0.9),axiom,file(pboole,cc2_pboole)]).

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(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(fc8_funcop_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_funcop_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B) )
     => ( v1_relat_1(k5_relat_1(B,A))
        & v1_funct_1(k5_relat_1(B,A))
        & v1_funcop_1(k5_relat_1(B,A)) ) ) ),
    file(funcop_1,fc8_funcop_1),
    [interesting(0.9),axiom,file(funcop_1,fc8_funcop_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(rc1_pboole,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v3_relat_1(A)
      & v1_funct_1(A) ) ),
    file(pboole,rc1_pboole),
    [interesting(0.9),axiom,file(pboole,rc1_pboole)]).

fof(rc2_pboole,theorem,(
    ! [A] : 
    ? [B] : 
      ( m1_pboole(B,A)
      & v1_relat_1(B)
      & v3_relat_1(B)
      & v1_funct_1(B) ) ),
    file(pboole,rc2_pboole),
    [interesting(0.9),axiom,file(pboole,rc2_pboole)]).

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

fof(rc4_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v3_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc4_funct_1),
    [interesting(0.9),axiom,file(funct_1,rc4_funct_1)]).

fof(t2_subset,theorem,(
    ! [A,B] : 
      ( m1_subset_1(A,B)
     => ( v1_xboole_0(B)
        | r2_hidden(A,B) ) ) ),
    file(subset,t2_subset),
    [interesting(0.9),axiom,file(subset,t2_subset)]).

fof(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(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(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_k1_partfun1,definition,(
    ! [A,B,C,D,E,F] : 
      ( ( v1_funct_1(E)
        & m1_relset_1(E,A,B)
        & v1_funct_1(F)
        & m1_relset_1(F,C,D) )
     => k1_partfun1(A,B,C,D,E,F) = k5_relat_1(E,F) ) ),
    file(partfun1,k1_partfun1),
    [interesting(0.9),axiom,file(partfun1,k1_partfun1)]).

fof(dt_k1_partfun1,axiom,(
    ! [A,B,C,D,E,F] : 
      ( ( v1_funct_1(E)
        & m1_relset_1(E,A,B)
        & v1_funct_1(F)
        & m1_relset_1(F,C,D) )
     => ( v1_funct_1(k1_partfun1(A,B,C,D,E,F))
        & m2_relset_1(k1_partfun1(A,B,C,D,E,F),A,D) ) ) ),
    file(partfun1,k1_partfun1),
    [interesting(0.9),axiom,file(partfun1,k1_partfun1)]).

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_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(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(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(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(de_c2_6_1__altcat_2,definition,(
    c2_6_1__altcat_2 = k1_funct_1(c6_6__altcat_2,c1_6_1__altcat_2) ),
    introduced(definition,[new_symbol(c2_6_1__altcat_2),file(altcat_2,c2_6_1__altcat_2)]),
    [interesting(0.65),axiom,file(altcat_2,c2_6_1__altcat_2)]).

fof(e3_6_1__altcat_2,plain,
    ( v1_funct_1(k1_funct_1(c6_6__altcat_2,c1_6_1__altcat_2))
    & v1_funct_2(k1_funct_1(c6_6__altcat_2,c1_6_1__altcat_2),k1_funct_1(c3_6__altcat_2,c1_6_1__altcat_2),k1_funct_1(c4_6__altcat_2,c1_6_1__altcat_2))
    & m2_relset_1(k1_funct_1(c6_6__altcat_2,c1_6_1__altcat_2),k1_funct_1(c3_6__altcat_2,c1_6_1__altcat_2),k1_funct_1(c4_6__altcat_2,c1_6_1__altcat_2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6__altcat_2,dt_c1_6_1__altcat_2,dt_c3_6__altcat_2,dt_c4_6__altcat_2,dt_c6_6__altcat_2,e1_6_1__altcat_2])],[cc1_pboole,fc2_pboole,rc3_pboole,rc5_funct_1,cc2_pboole,rc1_pboole,rc2_pboole,rc3_relat_1,rc4_funct_1,reflexivity_r1_tarski,dt_k1_xboole_0,fc12_relat_1,fc4_relat_1,rc3_funct_1,t8_boole,existence_m1_relset_1,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_m1_relset_1,dt_m1_subset_1,cc1_funct_1,cc1_relat_1,cc1_relset_1,cc2_funct_1,fc1_subset_1,fc4_subset_1,fc7_funcop_1,rc1_funcop_1,rc1_funct_1,rc1_relat_1,rc1_subset_1,rc2_funct_1,rc2_relat_1,rc2_subset_1,rc4_pboole,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,antisymmetry_r2_hidden,existence_m1_pboole,existence_m2_relset_1,existence_m3_pboole,redefinition_m2_relset_1,dt_k1_funct_1,dt_m1_pboole,dt_m2_relset_1,dt_m3_pboole,dt_c1_6__altcat_2,dt_c1_6_1__altcat_2,dt_c3_6__altcat_2,dt_c4_6__altcat_2,dt_c6_6__altcat_2,cc3_pboole,t1_subset,t7_boole,e1_6_1__altcat_2,d18_pboole]),
    [interesting(0.65),file(altcat_2,e3_6_1__altcat_2),[file(altcat_2,e3_6_1__altcat_2)]]).

fof(dt_c2_6_1__altcat_2,plain,
    ( v1_funct_1(c2_6_1__altcat_2)
    & v1_funct_2(c2_6_1__altcat_2,k1_funct_1(c3_6__altcat_2,c1_6_1__altcat_2),k1_funct_1(c4_6__altcat_2,c1_6_1__altcat_2))
    & m2_relset_1(c2_6_1__altcat_2,k1_funct_1(c3_6__altcat_2,c1_6_1__altcat_2),k1_funct_1(c4_6__altcat_2,c1_6_1__altcat_2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6__altcat_2,dt_c1_6_1__altcat_2,dt_c3_6__altcat_2,dt_c4_6__altcat_2,dt_c6_6__altcat_2,e1_6_1__altcat_2])],[cc1_pboole,fc2_pboole,rc3_pboole,rc5_funct_1,cc2_pboole,rc1_pboole,rc2_pboole,rc3_relat_1,rc4_funct_1,antisymmetry_r2_hidden,dt_k1_xboole_0,fc12_relat_1,fc4_relat_1,rc3_funct_1,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc4_subset_1,fc7_funcop_1,rc1_funcop_1,rc1_relat_1,rc1_subset_1,rc2_funct_1,rc2_relat_1,rc2_subset_1,rc4_pboole,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_pboole,existence_m1_relset_1,existence_m1_subset_1,existence_m3_pboole,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_m1_pboole,dt_m1_relset_1,dt_m1_subset_1,dt_m3_pboole,dt_c1_6__altcat_2,cc1_relset_1,cc3_pboole,fc1_subset_1,rc1_funct_1,t3_subset,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_funct_1,dt_m2_relset_1,dt_c1_6_1__altcat_2,dt_c3_6__altcat_2,dt_c4_6__altcat_2,dt_c6_6__altcat_2,de_c2_6_1__altcat_2,e3_6_1__altcat_2]),
    [interesting(0.65),file(altcat_2,c2_6_1__altcat_2),[file(altcat_2,c2_6_1__altcat_2)]]).

fof(de_c3_6_1__altcat_2,definition,(
    c3_6_1__altcat_2 = k1_funct_1(c5_6__altcat_2,c1_6_1__altcat_2) ),
    introduced(definition,[new_symbol(c3_6_1__altcat_2),file(altcat_2,c3_6_1__altcat_2)]),
    [interesting(0.65),axiom,file(altcat_2,c3_6_1__altcat_2)]).

fof(e4_6_1__altcat_2,plain,
    ( v1_funct_1(k1_funct_1(c5_6__altcat_2,c1_6_1__altcat_2))
    & v1_funct_2(k1_funct_1(c5_6__altcat_2,c1_6_1__altcat_2),k1_funct_1(c2_6__altcat_2,c1_6_1__altcat_2),k1_funct_1(c3_6__altcat_2,c1_6_1__altcat_2))
    & m2_relset_1(k1_funct_1(c5_6__altcat_2,c1_6_1__altcat_2),k1_funct_1(c2_6__altcat_2,c1_6_1__altcat_2),k1_funct_1(c3_6__altcat_2,c1_6_1__altcat_2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6__altcat_2,dt_c1_6_1__altcat_2,dt_c2_6__altcat_2,dt_c3_6__altcat_2,dt_c5_6__altcat_2,e1_6_1__altcat_2])],[cc1_pboole,fc2_pboole,rc3_pboole,rc5_funct_1,cc2_pboole,rc1_pboole,rc2_pboole,rc3_relat_1,rc4_funct_1,reflexivity_r1_tarski,dt_k1_xboole_0,fc12_relat_1,fc4_relat_1,rc3_funct_1,t8_boole,existence_m1_relset_1,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_m1_relset_1,dt_m1_subset_1,cc1_funct_1,cc1_relat_1,cc1_relset_1,cc2_funct_1,fc1_subset_1,fc4_subset_1,fc7_funcop_1,rc1_funcop_1,rc1_funct_1,rc1_relat_1,rc1_subset_1,rc2_funct_1,rc2_relat_1,rc2_subset_1,rc4_pboole,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,antisymmetry_r2_hidden,existence_m1_pboole,existence_m2_relset_1,existence_m3_pboole,redefinition_m2_relset_1,dt_k1_funct_1,dt_m1_pboole,dt_m2_relset_1,dt_m3_pboole,dt_c1_6__altcat_2,dt_c1_6_1__altcat_2,dt_c2_6__altcat_2,dt_c3_6__altcat_2,dt_c5_6__altcat_2,cc3_pboole,t1_subset,t7_boole,e1_6_1__altcat_2,d18_pboole]),
    [interesting(0.65),file(altcat_2,e4_6_1__altcat_2),[file(altcat_2,e4_6_1__altcat_2)]]).

fof(dt_c3_6_1__altcat_2,plain,
    ( v1_funct_1(c3_6_1__altcat_2)
    & v1_funct_2(c3_6_1__altcat_2,k1_funct_1(c2_6__altcat_2,c1_6_1__altcat_2),k1_funct_1(c3_6__altcat_2,c1_6_1__altcat_2))
    & m2_relset_1(c3_6_1__altcat_2,k1_funct_1(c2_6__altcat_2,c1_6_1__altcat_2),k1_funct_1(c3_6__altcat_2,c1_6_1__altcat_2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6__altcat_2,dt_c1_6_1__altcat_2,dt_c2_6__altcat_2,dt_c3_6__altcat_2,dt_c5_6__altcat_2,e1_6_1__altcat_2])],[cc1_pboole,fc2_pboole,rc3_pboole,rc5_funct_1,cc2_pboole,rc1_pboole,rc2_pboole,rc3_relat_1,rc4_funct_1,antisymmetry_r2_hidden,dt_k1_xboole_0,fc12_relat_1,fc4_relat_1,rc3_funct_1,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc4_subset_1,fc7_funcop_1,rc1_funcop_1,rc1_relat_1,rc1_subset_1,rc2_funct_1,rc2_relat_1,rc2_subset_1,rc4_pboole,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_pboole,existence_m1_relset_1,existence_m1_subset_1,existence_m3_pboole,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_m1_pboole,dt_m1_relset_1,dt_m1_subset_1,dt_m3_pboole,dt_c1_6__altcat_2,cc1_relset_1,cc3_pboole,fc1_subset_1,rc1_funct_1,t3_subset,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_funct_1,dt_m2_relset_1,dt_c1_6_1__altcat_2,dt_c2_6__altcat_2,dt_c3_6__altcat_2,dt_c5_6__altcat_2,de_c3_6_1__altcat_2,e4_6_1__altcat_2]),
    [interesting(0.65),file(altcat_2,c3_6_1__altcat_2),[file(altcat_2,c3_6_1__altcat_2)]]).

fof(t2_boole,theorem,(
    ! [A] : k3_xboole_0(A,k1_xboole_0) = k1_xboole_0 ),
    file(boole,t2_boole),
    [interesting(0.9),axiom,file(boole,t2_boole)]).

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(commutativity_k3_xboole_0,theorem,(
    ! [A,B] : k3_xboole_0(A,B) = k3_xboole_0(B,A) ),
    file(xboole_0,k3_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k3_xboole_0)]).

fof(idempotence_k3_xboole_0,theorem,(
    ! [A,B] : k3_xboole_0(A,A) = A ),
    file(xboole_0,k3_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k3_xboole_0)]).

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_k3_xboole_0,axiom,(
    $true ),
    file(xboole_0,k3_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k3_xboole_0)]).

fof(fc1_relat_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_relat_1(B) )
     => v1_relat_1(k3_xboole_0(A,B)) ) ),
    file(relat_1,fc1_relat_1),
    [interesting(0.9),axiom,file(relat_1,fc1_relat_1)]).

fof(d3_pboole,definition,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( m1_pboole(B,A)
      <=> k1_relat_1(B) = A ) ) ),
    file(pboole,d3_pboole),
    [interesting(0.9),axiom,file(pboole,d3_pboole)]).

fof(e5_6_1__altcat_2,plain,(
    r2_hidden(c1_6_1__altcat_2,k1_relat_1(c7_6__altcat_2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6_1__altcat_2,dt_c2_6__altcat_2,dt_c3_6__altcat_2,dt_c4_6__altcat_2,dt_c1_6__altcat_2,dt_c5_6__altcat_2,dt_c6_6__altcat_2,e1_6_1__altcat_2])],[cc1_pboole,rc3_pboole,rc5_funct_1,cc2_pboole,rc1_pboole,rc2_pboole,rc3_relat_1,rc4_funct_1,existence_m3_pboole,dt_k1_xboole_0,dt_m3_pboole,dt_c2_6__altcat_2,dt_c3_6__altcat_2,dt_c4_6__altcat_2,cc3_pboole,fc12_relat_1,fc4_relat_1,rc3_funct_1,existence_m1_subset_1,dt_k13_pboole,dt_m1_subset_1,dt_c5_6__altcat_2,dt_c6_6__altcat_2,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc5_relat_1,fc7_relat_1,rc1_funcop_1,rc1_relat_1,rc2_funct_1,rc2_relat_1,rc4_pboole,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,existence_m1_pboole,dt_k1_relat_1,dt_m1_pboole,dt_c1_6__altcat_2,dt_c1_6_1__altcat_2,dt_c7_6__altcat_2,de_c7_6__altcat_2,rc1_funct_1,t1_subset,t7_boole,e1_6_1__altcat_2,d3_pboole]),
    [interesting(0.65),file(altcat_2,e5_6_1__altcat_2),[file(altcat_2,e5_6_1__altcat_2)]]).

fof(d24_pboole,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_funcop_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_funcop_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_funcop_1(C) )
             => ( C = k13_pboole(A,B)
              <=> ( k1_relat_1(C) = k3_xboole_0(k1_relat_1(A),k1_relat_1(B))
                  & ! [D] : 
                      ( r2_hidden(D,k1_relat_1(C))
                     => k1_funct_1(C,D) = k5_relat_1(k1_funct_1(A,D),k1_funct_1(B,D)) ) ) ) ) ) ) ),
    file(pboole,d24_pboole),
    [interesting(0.9),axiom,file(pboole,d24_pboole)]).

fof(e6_6_1__altcat_2,plain,(
    k1_funct_1(k13_pboole(c5_6__altcat_2,c6_6__altcat_2),c1_6_1__altcat_2) = k5_relat_1(c3_6_1__altcat_2,c2_6_1__altcat_2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6_1__altcat_2,dt_c2_6__altcat_2,dt_c3_6__altcat_2,dt_c4_6__altcat_2,dt_c1_6__altcat_2,dt_c5_6__altcat_2,dt_c6_6__altcat_2,e1_6_1__altcat_2])],[cc1_pboole,fc2_pboole,rc3_pboole,rc5_funct_1,reflexivity_r1_tarski,cc2_pboole,rc1_pboole,rc2_pboole,rc3_relat_1,rc4_funct_1,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,fc4_relat_1,fc4_subset_1,rc1_subset_1,rc2_subset_1,rc3_funct_1,t2_boole,t3_subset,t4_subset,t5_subset,existence_m1_pboole,existence_m1_subset_1,existence_m2_relset_1,existence_m3_pboole,redefinition_m2_relset_1,dt_m1_pboole,dt_m1_subset_1,dt_m2_relset_1,dt_m3_pboole,dt_c1_6__altcat_2,dt_c2_6__altcat_2,dt_c3_6__altcat_2,dt_c4_6__altcat_2,cc1_funct_1,cc1_relat_1,cc2_funct_1,cc3_pboole,fc10_relat_1,fc5_relat_1,fc7_relat_1,fc9_relat_1,rc1_relat_1,rc2_funct_1,rc2_relat_1,rc4_pboole,t2_subset,t6_boole,t8_boole,commutativity_k3_xboole_0,idempotence_k3_xboole_0,antisymmetry_r2_hidden,dt_k13_pboole,dt_k1_funct_1,dt_k1_relat_1,dt_k3_xboole_0,dt_k5_relat_1,dt_c1_6_1__altcat_2,dt_c2_6_1__altcat_2,dt_c3_6_1__altcat_2,dt_c5_6__altcat_2,dt_c6_6__altcat_2,dt_c7_6__altcat_2,de_c2_6_1__altcat_2,de_c3_6_1__altcat_2,de_c7_6__altcat_2,fc1_funct_1,fc1_relat_1,fc7_funcop_1,fc8_funcop_1,rc1_funcop_1,rc1_funct_1,t1_subset,t7_boole,e5_6_1__altcat_2,d24_pboole]),
    [interesting(0.65),file(altcat_2,e6_6_1__altcat_2),[file(altcat_2,e6_6_1__altcat_2)]]).

fof(reflexivity_r1_pzfmisc1,theorem,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => r1_pzfmisc1(A,B,B) ) ),
    file(pzfmisc1,r1_pzfmisc1),
    [interesting(0.9),axiom,file(pzfmisc1,r1_pzfmisc1)]).

fof(d3_pzfmisc1,definition,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ( r1_pzfmisc1(A,B,C)
          <=> ! [D] : 
                ( ( r2_hidden(D,A)
                  & k1_funct_1(C,D) = k1_xboole_0 )
               => k1_funct_1(B,D) = k1_xboole_0 ) ) ) ) ),
    file(pzfmisc1,d3_pzfmisc1),
    [interesting(0.9),axiom,file(pzfmisc1,d3_pzfmisc1)]).

fof(e2_6_1__altcat_2,plain,
    ( k1_funct_1(c3_6__altcat_2,c1_6_1__altcat_2) = k1_xboole_0
   => k1_funct_1(c2_6__altcat_2,c1_6_1__altcat_2) = k1_xboole_0 ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6__altcat_2,dt_c1_6_1__altcat_2,dt_c2_6__altcat_2,dt_c3_6__altcat_2,e1_6_1__altcat_2,e1_6__altcat_2])],[cc1_pboole,fc2_pboole,rc3_funct_1,rc3_pboole,rc5_funct_1,existence_m1_subset_1,dt_m1_subset_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,cc2_pboole,rc1_funct_1,rc1_pboole,rc1_relat_1,rc2_funct_1,rc2_pboole,rc2_relat_1,rc3_relat_1,rc4_funct_1,t2_subset,t8_boole,reflexivity_r1_pzfmisc1,antisymmetry_r2_hidden,existence_m1_pboole,dt_k1_funct_1,dt_k1_xboole_0,dt_m1_pboole,dt_c1_6__altcat_2,dt_c1_6_1__altcat_2,dt_c2_6__altcat_2,dt_c3_6__altcat_2,fc12_relat_1,fc4_relat_1,t1_subset,t6_boole,t7_boole,e1_6_1__altcat_2,e1_6__altcat_2,d3_pzfmisc1]),
    [interesting(0.65),file(altcat_2,e2_6_1__altcat_2),[file(altcat_2,e2_6_1__altcat_2)]]).

fof(t19_funct_2,theorem,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m2_relset_1(D,A,B) )
     => ! [E] : 
          ( ( v1_funct_1(E)
            & v1_funct_2(E,B,C)
            & m2_relset_1(E,B,C) )
         => ( ~ ( B = k1_xboole_0
                & C != k1_xboole_0
                & A != k1_xboole_0 )
           => ( v1_funct_1(k1_partfun1(A,B,B,C,D,E))
              & v1_funct_2(k1_partfun1(A,B,B,C,D,E),A,C)
              & m2_relset_1(k1_partfun1(A,B,B,C,D,E),A,C) ) ) ) ) ),
    file(funct_2,t19_funct_2),
    [interesting(0.9),axiom,file(funct_2,t19_funct_2)]).

fof(e7_6_1__altcat_2,plain,
    ( v1_funct_1(k1_funct_1(c7_6__altcat_2,c1_6_1__altcat_2))
    & v1_funct_2(k1_funct_1(c7_6__altcat_2,c1_6_1__altcat_2),k1_funct_1(c2_6__altcat_2,c1_6_1__altcat_2),k1_funct_1(c4_6__altcat_2,c1_6_1__altcat_2))
    & m2_relset_1(k1_funct_1(c7_6__altcat_2,c1_6_1__altcat_2),k1_funct_1(c2_6__altcat_2,c1_6_1__altcat_2),k1_funct_1(c4_6__altcat_2,c1_6_1__altcat_2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c4_6__altcat_2,dt_c5_6__altcat_2,dt_c6_6__altcat_2,dt_c1_6__altcat_2,dt_c1_6_1__altcat_2,dt_c2_6__altcat_2,dt_c3_6__altcat_2,e1_6_1__altcat_2,e1_6__altcat_2])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,cc1_pboole,fc2_pboole,rc3_funct_1,rc3_pboole,rc5_funct_1,t1_subset,t4_subset,t5_subset,existence_m1_pboole,existence_m1_relset_1,existence_m1_subset_1,existence_m3_pboole,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_m1_pboole,dt_m1_relset_1,dt_m1_subset_1,dt_m3_pboole,dt_c1_6__altcat_2,cc1_funct_1,cc1_relat_1,cc1_relset_1,cc2_funct_1,cc2_pboole,cc3_pboole,fc10_relat_1,fc1_funct_1,fc1_subset_1,fc4_subset_1,fc7_funcop_1,fc8_funcop_1,fc9_relat_1,rc1_funcop_1,rc1_funct_1,rc1_pboole,rc1_relat_1,rc1_subset_1,rc2_funct_1,rc2_pboole,rc2_relat_1,rc2_subset_1,rc3_relat_1,rc4_funct_1,rc4_pboole,t2_subset,t3_subset,t7_boole,t8_boole,existence_m2_relset_1,redefinition_k1_partfun1,redefinition_m2_relset_1,dt_k13_pboole,dt_k1_funct_1,dt_k1_partfun1,dt_k1_xboole_0,dt_k5_relat_1,dt_m2_relset_1,dt_c1_6_1__altcat_2,dt_c2_6__altcat_2,dt_c2_6_1__altcat_2,dt_c3_6__altcat_2,dt_c3_6_1__altcat_2,dt_c4_6__altcat_2,dt_c5_6__altcat_2,dt_c6_6__altcat_2,dt_c7_6__altcat_2,de_c2_6_1__altcat_2,de_c3_6_1__altcat_2,de_c7_6__altcat_2,fc12_relat_1,fc4_relat_1,t6_boole,e6_6_1__altcat_2,e2_6_1__altcat_2,t19_funct_2]),
    [interesting(0.65),file(altcat_2,e7_6_1__altcat_2),[file(altcat_2,e7_6_1__altcat_2)]]).

fof(i3_6_1__altcat_2,theorem,(
    $true ),
    introduced(tautology,[file(altcat_2,i3_6_1__altcat_2)]),
    [interesting(0.65),trivial,file(altcat_2,i3_6_1__altcat_2)]).

fof(i2_6_1__altcat_2,plain,
    ( v1_funct_1(k1_funct_1(c7_6__altcat_2,c1_6_1__altcat_2))
    & v1_funct_2(k1_funct_1(c7_6__altcat_2,c1_6_1__altcat_2),k1_funct_1(c2_6__altcat_2,c1_6_1__altcat_2),k1_funct_1(c4_6__altcat_2,c1_6_1__altcat_2))
    & m2_relset_1(k1_funct_1(c7_6__altcat_2,c1_6_1__altcat_2),k1_funct_1(c2_6__altcat_2,c1_6_1__altcat_2),k1_funct_1(c4_6__altcat_2,c1_6_1__altcat_2)) ),
    inference(conclusion,[status(thm),assumptions([dt_c4_6__altcat_2,dt_c5_6__altcat_2,dt_c6_6__altcat_2,dt_c1_6__altcat_2,dt_c1_6_1__altcat_2,dt_c2_6__altcat_2,dt_c3_6__altcat_2,e1_6_1__altcat_2,e1_6__altcat_2])],[e7_6_1__altcat_2,i3_6_1__altcat_2]),
    [interesting(0.65),file(altcat_2,i2_6_1__altcat_2),[file(altcat_2,i2_6_1__altcat_2)]]).

fof(i1_6_1__altcat_2,plain,(
    ~ ( r2_hidden(c1_6_1__altcat_2,c1_6__altcat_2)
      & ~ ( v1_funct_1(k1_funct_1(c7_6__altcat_2,c1_6_1__altcat_2))
          & v1_funct_2(k1_funct_1(c7_6__altcat_2,c1_6_1__altcat_2),k1_funct_1(c2_6__altcat_2,c1_6_1__altcat_2),k1_funct_1(c4_6__altcat_2,c1_6_1__altcat_2))
          & m2_relset_1(k1_funct_1(c7_6__altcat_2,c1_6_1__altcat_2),k1_funct_1(c2_6__altcat_2,c1_6_1__altcat_2),k1_funct_1(c4_6__altcat_2,c1_6_1__altcat_2)) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c4_6__altcat_2,dt_c5_6__altcat_2,dt_c6_6__altcat_2,dt_c1_6__altcat_2,dt_c1_6_1__altcat_2,dt_c2_6__altcat_2,dt_c3_6__altcat_2,e1_6__altcat_2]),discharge_asm(discharge,[e1_6_1__altcat_2])],[e1_6_1__altcat_2,i2_6_1__altcat_2]),
    [interesting(0.65),file(altcat_2,i1_6_1__altcat_2),[file(altcat_2,i1_6_1__altcat_2)]]).

fof(i1_6_1_tmp__altcat_2,plain,(
    ~ ( r2_hidden(c1_6_1__altcat_2,c1_6__altcat_2)
      & ~ ( v1_funct_1(k1_funct_1(c7_6__altcat_2,c1_6_1__altcat_2))
          & v1_funct_2(k1_funct_1(c7_6__altcat_2,c1_6_1__altcat_2),k1_funct_1(c2_6__altcat_2,c1_6_1__altcat_2),k1_funct_1(c4_6__altcat_2,c1_6_1__altcat_2))
          & m2_relset_1(k1_funct_1(c7_6__altcat_2,c1_6_1__altcat_2),k1_funct_1(c2_6__altcat_2,c1_6_1__altcat_2),k1_funct_1(c4_6__altcat_2,c1_6_1__altcat_2)) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c4_6__altcat_2,dt_c5_6__altcat_2,dt_c6_6__altcat_2,dt_c1_6__altcat_2,dt_c2_6__altcat_2,dt_c3_6__altcat_2,e1_6__altcat_2]),discharge_asm(discharge,[dt_c1_6_1__altcat_2])],[dt_c1_6_1__altcat_2,i1_6_1__altcat_2]),
    [interesting(0.8),e3_6__altcat_2]).

fof(e3_6__altcat_2,plain,(
    m3_pboole(c7_6__altcat_2,c1_6__altcat_2,c2_6__altcat_2,c4_6__altcat_2) ),
    inference(let,[status(thm),assumptions([dt_c4_6__altcat_2,dt_c5_6__altcat_2,dt_c6_6__altcat_2,dt_c1_6__altcat_2,dt_c2_6__altcat_2,dt_c3_6__altcat_2,e1_6__altcat_2])],[i1_6_1_tmp__altcat_2,rc3_funct_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc4_subset_1,rc1_relat_1,rc1_subset_1,rc2_funct_1,rc2_relat_1,rc2_subset_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_m1_relset_1,dt_m1_subset_1,cc1_relset_1,fc1_subset_1,fc7_funcop_1,rc1_funcop_1,rc1_funct_1,rc4_pboole,antisymmetry_r2_hidden,redefinition_m2_relset_1,dt_k1_funct_1,dt_m1_pboole,dt_m2_relset_1,dt_m3_pboole,dt_c1_6__altcat_2,dt_c2_6__altcat_2,dt_c4_6__altcat_2,dt_c7_6__altcat_2,cc3_pboole,d18_pboole,dh_c1_6_1__altcat_2]),
    [interesting(0.8),file(altcat_2,e3_6__altcat_2),[file(altcat_2,e3_6__altcat_2)]]).

fof(e4_6__altcat_2,plain,(
    m3_pboole(k13_pboole(c5_6__altcat_2,c6_6__altcat_2),c1_6__altcat_2,c2_6__altcat_2,c4_6__altcat_2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c4_6__altcat_2,dt_c5_6__altcat_2,dt_c6_6__altcat_2,dt_c1_6__altcat_2,dt_c2_6__altcat_2,dt_c3_6__altcat_2,e1_6__altcat_2])],[existence_m1_pboole,dt_m1_pboole,dt_c3_6__altcat_2,cc3_pboole,rc1_funcop_1,rc1_funct_1,rc4_pboole,existence_m3_pboole,dt_k13_pboole,dt_m3_pboole,dt_c1_6__altcat_2,dt_c2_6__altcat_2,dt_c4_6__altcat_2,dt_c5_6__altcat_2,dt_c6_6__altcat_2,dt_c7_6__altcat_2,de_c7_6__altcat_2,e3_6__altcat_2]),
    [interesting(0.8),file(altcat_2,e4_6__altcat_2),[file(altcat_2,e4_6__altcat_2)]]).

fof(i6_6__altcat_2,theorem,(
    $true ),
    introduced(tautology,[file(altcat_2,i6_6__altcat_2)]),
    [interesting(0.8),trivial,file(altcat_2,i6_6__altcat_2)]).

fof(i5_6__altcat_2,plain,(
    m3_pboole(k13_pboole(c5_6__altcat_2,c6_6__altcat_2),c1_6__altcat_2,c2_6__altcat_2,c4_6__altcat_2) ),
    inference(conclusion,[status(thm),assumptions([dt_c4_6__altcat_2,dt_c5_6__altcat_2,dt_c6_6__altcat_2,dt_c1_6__altcat_2,dt_c2_6__altcat_2,dt_c3_6__altcat_2,e1_6__altcat_2])],[e4_6__altcat_2,i6_6__altcat_2]),
    [interesting(0.8),file(altcat_2,i5_6__altcat_2),[file(altcat_2,i5_6__altcat_2)]]).

fof(i5_6_tmp__altcat_2,plain,
    ( m3_pboole(c6_6__altcat_2,c1_6__altcat_2,c3_6__altcat_2,c4_6__altcat_2)
   => m3_pboole(k13_pboole(c5_6__altcat_2,c6_6__altcat_2),c1_6__altcat_2,c2_6__altcat_2,c4_6__altcat_2) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c4_6__altcat_2,dt_c5_6__altcat_2,dt_c1_6__altcat_2,dt_c2_6__altcat_2,dt_c3_6__altcat_2,e1_6__altcat_2]),discharge_asm(discharge,[dt_c6_6__altcat_2])],[dt_c6_6__altcat_2,i5_6__altcat_2]),
    [interesting(0.8),i4_6__altcat_2]).

fof(i4_6__altcat_2,plain,(
    ! [A] : 
      ( m3_pboole(A,c1_6__altcat_2,c3_6__altcat_2,c4_6__altcat_2)
     => m3_pboole(k13_pboole(c5_6__altcat_2,A),c1_6__altcat_2,c2_6__altcat_2,c4_6__altcat_2) ) ),
    inference(let,[status(thm),assumptions([dt_c4_6__altcat_2,dt_c5_6__altcat_2,dt_c1_6__altcat_2,dt_c2_6__altcat_2,dt_c3_6__altcat_2,e1_6__altcat_2])],[i5_6_tmp__altcat_2,dh_c6_6__altcat_2]),
    [interesting(0.8),file(altcat_2,i4_6__altcat_2),[file(altcat_2,i4_6__altcat_2)]]).

fof(i4_6_tmp__altcat_2,plain,
    ( m3_pboole(c5_6__altcat_2,c1_6__altcat_2,c2_6__altcat_2,c3_6__altcat_2)
   => ! [A] : 
        ( m3_pboole(A,c1_6__altcat_2,c3_6__altcat_2,c4_6__altcat_2)
       => m3_pboole(k13_pboole(c5_6__altcat_2,A),c1_6__altcat_2,c2_6__altcat_2,c4_6__altcat_2) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c4_6__altcat_2,dt_c1_6__altcat_2,dt_c2_6__altcat_2,dt_c3_6__altcat_2,e1_6__altcat_2]),discharge_asm(discharge,[dt_c5_6__altcat_2])],[dt_c5_6__altcat_2,i4_6__altcat_2]),
    [interesting(0.8),i3_6__altcat_2]).

fof(i3_6__altcat_2,plain,(
    ! [A] : 
      ( m3_pboole(A,c1_6__altcat_2,c2_6__altcat_2,c3_6__altcat_2)
     => ! [B] : 
          ( m3_pboole(B,c1_6__altcat_2,c3_6__altcat_2,c4_6__altcat_2)
         => m3_pboole(k13_pboole(A,B),c1_6__altcat_2,c2_6__altcat_2,c4_6__altcat_2) ) ) ),
    inference(let,[status(thm),assumptions([dt_c4_6__altcat_2,dt_c1_6__altcat_2,dt_c2_6__altcat_2,dt_c3_6__altcat_2,e1_6__altcat_2])],[i4_6_tmp__altcat_2,dh_c5_6__altcat_2]),
    [interesting(0.8),file(altcat_2,i3_6__altcat_2),[file(altcat_2,i3_6__altcat_2)]]).

fof(i2_6__altcat_2,plain,
    ( r1_pzfmisc1(c1_6__altcat_2,c2_6__altcat_2,c3_6__altcat_2)
   => ! [A] : 
        ( m3_pboole(A,c1_6__altcat_2,c2_6__altcat_2,c3_6__altcat_2)
       => ! [B] : 
            ( m3_pboole(B,c1_6__altcat_2,c3_6__altcat_2,c4_6__altcat_2)
           => m3_pboole(k13_pboole(A,B),c1_6__altcat_2,c2_6__altcat_2,c4_6__altcat_2) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c4_6__altcat_2,dt_c1_6__altcat_2,dt_c2_6__altcat_2,dt_c3_6__altcat_2]),discharge_asm(discharge,[e1_6__altcat_2])],[e1_6__altcat_2,i3_6__altcat_2]),
    [interesting(0.8),file(altcat_2,i2_6__altcat_2),[file(altcat_2,i2_6__altcat_2)]]).

fof(i2_6_tmp__altcat_2,plain,
    ( ( m1_pboole(c2_6__altcat_2,c1_6__altcat_2)
      & m1_pboole(c3_6__altcat_2,c1_6__altcat_2)
      & m1_pboole(c4_6__altcat_2,c1_6__altcat_2) )
   => ( r1_pzfmisc1(c1_6__altcat_2,c2_6__altcat_2,c3_6__altcat_2)
     => ! [A] : 
          ( m3_pboole(A,c1_6__altcat_2,c2_6__altcat_2,c3_6__altcat_2)
         => ! [B] : 
              ( m3_pboole(B,c1_6__altcat_2,c3_6__altcat_2,c4_6__altcat_2)
             => m3_pboole(k13_pboole(A,B),c1_6__altcat_2,c2_6__altcat_2,c4_6__altcat_2) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_6__altcat_2]),discharge_asm(discharge,[dt_c2_6__altcat_2,dt_c3_6__altcat_2,dt_c4_6__altcat_2])],[dt_c2_6__altcat_2,dt_c3_6__altcat_2,dt_c4_6__altcat_2,i2_6__altcat_2]),
    [interesting(0.8),i1_6__altcat_2]).

fof(i1_6__altcat_2,plain,(
    ! [A] : 
      ( m1_pboole(A,c1_6__altcat_2)
     => ! [B] : 
          ( m1_pboole(B,c1_6__altcat_2)
         => ! [C] : 
              ( m1_pboole(C,c1_6__altcat_2)
             => ( r1_pzfmisc1(c1_6__altcat_2,A,B)
               => ! [D] : 
                    ( m3_pboole(D,c1_6__altcat_2,A,B)
                   => ! [E] : 
                        ( m3_pboole(E,c1_6__altcat_2,B,C)
                       => m3_pboole(k13_pboole(D,E),c1_6__altcat_2,A,C) ) ) ) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_6__altcat_2])],[i2_6_tmp__altcat_2,dh_c2_6__altcat_2,dh_c3_6__altcat_2,dh_c4_6__altcat_2]),
    [interesting(0.8),file(altcat_2,i1_6__altcat_2),[file(altcat_2,i1_6__altcat_2)]]).

fof(i1_6_tmp__altcat_2,plain,(
    ! [A] : 
      ( m1_pboole(A,c1_6__altcat_2)
     => ! [B] : 
          ( m1_pboole(B,c1_6__altcat_2)
         => ! [C] : 
              ( m1_pboole(C,c1_6__altcat_2)
             => ( r1_pzfmisc1(c1_6__altcat_2,A,B)
               => ! [D] : 
                    ( m3_pboole(D,c1_6__altcat_2,A,B)
                   => ! [E] : 
                        ( m3_pboole(E,c1_6__altcat_2,B,C)
                       => m3_pboole(k13_pboole(D,E),c1_6__altcat_2,A,C) ) ) ) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_6__altcat_2])],[dt_c1_6__altcat_2,i1_6__altcat_2]),
    [interesting(1),t4_altcat_2]).

fof(t4_altcat_2,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m1_pboole(D,A)
             => ( r1_pzfmisc1(A,B,C)
               => ! [E] : 
                    ( m3_pboole(E,A,B,C)
                   => ! [F] : 
                        ( m3_pboole(F,A,C,D)
                       => m3_pboole(k13_pboole(E,F),A,B,D) ) ) ) ) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_6_tmp__altcat_2,dh_c1_6__altcat_2]),
    [interesting(1),file(altcat_2,t4_altcat_2),[file(altcat_2,t4_altcat_2)]]).