% Mizar ND problem: t5_altcat_1,altcat_1,97,24 
fof(dh_c1_7__altcat_1,definition,
    ( ! [A,B] : 
        ~ ( k1_funct_2(c1_7__altcat_1,A) != k1_xboole_0
          & k1_funct_2(A,B) != k1_xboole_0
          & k1_funct_2(c1_7__altcat_1,B) = k1_xboole_0 )
   => ! [C,D,E] : 
        ~ ( k1_funct_2(C,D) != k1_xboole_0
          & k1_funct_2(D,E) != k1_xboole_0
          & k1_funct_2(C,E) = k1_xboole_0 ) ),
    introduced(definition,[new_symbol(c1_7__altcat_1),file(altcat_1,c1_7__altcat_1)]),
    [interesting(0.8),axiom,file(altcat_1,c1_7__altcat_1)]).

fof(dh_c2_7__altcat_1,definition,
    ( ! [A] : 
        ~ ( k1_funct_2(c1_7__altcat_1,c2_7__altcat_1) != k1_xboole_0
          & k1_funct_2(c2_7__altcat_1,A) != k1_xboole_0
          & k1_funct_2(c1_7__altcat_1,A) = k1_xboole_0 )
   => ! [B,C] : 
        ~ ( k1_funct_2(c1_7__altcat_1,B) != k1_xboole_0
          & k1_funct_2(B,C) != k1_xboole_0
          & k1_funct_2(c1_7__altcat_1,C) = k1_xboole_0 ) ),
    introduced(definition,[new_symbol(c2_7__altcat_1),file(altcat_1,c2_7__altcat_1)]),
    [interesting(0.8),axiom,file(altcat_1,c2_7__altcat_1)]).

fof(dh_c3_7__altcat_1,definition,
    ( ~ ( k1_funct_2(c1_7__altcat_1,c2_7__altcat_1) != k1_xboole_0
        & k1_funct_2(c2_7__altcat_1,c3_7__altcat_1) != k1_xboole_0
        & k1_funct_2(c1_7__altcat_1,c3_7__altcat_1) = k1_xboole_0 )
   => ! [A] : 
        ~ ( k1_funct_2(c1_7__altcat_1,c2_7__altcat_1) != k1_xboole_0
          & k1_funct_2(c2_7__altcat_1,A) != k1_xboole_0
          & k1_funct_2(c1_7__altcat_1,A) = k1_xboole_0 ) ),
    introduced(definition,[new_symbol(c3_7__altcat_1),file(altcat_1,c3_7__altcat_1)]),
    [interesting(0.8),axiom,file(altcat_1,c3_7__altcat_1)]).

fof(e1_7__altcat_1,assumption,(
    k1_funct_2(c1_7__altcat_1,c2_7__altcat_1) != k1_xboole_0 ),
    introduced(assumption,[file(altcat_1,e1_7__altcat_1)]),
    [interesting(0.8),axiom,file(altcat_1,e1_7__altcat_1)]).

fof(e2_7__altcat_1,assumption,(
    k1_funct_2(c2_7__altcat_1,c3_7__altcat_1) != k1_xboole_0 ),
    introduced(assumption,[file(altcat_1,e2_7__altcat_1)]),
    [interesting(0.8),axiom,file(altcat_1,e2_7__altcat_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(cc1_funct_2,theorem,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => ( ( v1_funct_1(C)
          & v1_partfun1(C,A,B) )
       => ( v1_funct_1(C)
          & v1_funct_2(C,A,B) ) ) ) ),
    file(funct_2,cc1_funct_2),
    [interesting(0.9),axiom,file(funct_2,cc1_funct_2)]).

fof(cc1_tex_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( ~ v1_tex_2(B,k1_zfmisc_1(A))
           => ~ v1_xboole_0(B) ) ) ) ),
    file(tex_2,cc1_tex_2),
    [interesting(0.9),axiom,file(tex_2,cc1_tex_2)]).

fof(rc2_tex_2,theorem,(
    ! [A] : 
    ? [B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
      & ~ v1_tex_2(B,k1_zfmisc_1(A)) ) ),
    file(tex_2,rc2_tex_2),
    [interesting(0.9),axiom,file(tex_2,rc2_tex_2)]).

fof(rc3_tex_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & v1_tex_2(B,k1_zfmisc_1(A)) ) ) ),
    file(tex_2,rc3_tex_2),
    [interesting(0.9),axiom,file(tex_2,rc3_tex_2)]).

fof(rc4_tex_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & ~ v1_tex_2(B,k1_zfmisc_1(A)) ) ) ),
    file(tex_2,rc4_tex_2),
    [interesting(0.9),axiom,file(tex_2,rc4_tex_2)]).

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_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(cc1_altcat_1,theorem,(
    ! [A] : 
      ( v1_fraenkel(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => v1_fraenkel(B) ) ) ),
    file(altcat_1,cc1_altcat_1),
    [interesting(0.9),axiom,file(altcat_1,cc1_altcat_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_tex_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_xboole_0(B)
           => v1_tex_2(B,k1_zfmisc_1(A)) ) ) ) ),
    file(tex_2,cc2_tex_2),
    [interesting(0.9),axiom,file(tex_2,cc2_tex_2)]).

fof(cc5_funct_2,theorem,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => ! [C] : 
          ( m1_relset_1(C,A,B)
         => ( ( v1_funct_1(C)
              & v1_funct_2(C,A,B) )
           => ( v1_funct_1(C)
              & v1_partfun1(C,A,B)
              & v1_funct_2(C,A,B) ) ) ) ) ),
    file(funct_2,cc5_funct_2),
    [interesting(0.9),axiom,file(funct_2,cc5_funct_2)]).

fof(cc6_funct_2,theorem,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ! [C] : 
          ( m1_relset_1(C,A,B)
         => ( ( v1_funct_1(C)
              & v1_funct_2(C,A,B) )
           => ( v1_funct_1(C)
              & ~ v1_xboole_0(C)
              & v1_partfun1(C,A,B)
              & v1_funct_2(C,A,B) ) ) ) ) ),
    file(funct_2,cc6_funct_2),
    [interesting(0.9),axiom,file(funct_2,cc6_funct_2)]).

fof(fc1_subset_1,theorem,(
    ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ),
    file(subset_1,fc1_subset_1),
    [interesting(0.9),axiom,file(subset_1,fc1_subset_1)]).

fof(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_2,theorem,(
    ! [A,B] : 
    ? [C] : 
      ( m1_relset_1(C,A,B)
      & v1_relat_1(C)
      & v1_funct_1(C)
      & v1_funct_2(C,A,B) ) ),
    file(funct_2,rc1_funct_2),
    [interesting(0.9),axiom,file(funct_2,rc1_funct_2)]).

fof(rc1_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(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_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(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_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_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_c2_7__altcat_1,assumption,(
    $true ),
    introduced(assumption,[file(altcat_1,c2_7__altcat_1)]),
    [interesting(0.8),axiom,file(altcat_1,c2_7__altcat_1)]).

fof(dh_c4_7__altcat_1,definition,
    ( ? [A] : r2_hidden(A,k1_funct_2(c1_7__altcat_1,c2_7__altcat_1))
   => r2_hidden(c4_7__altcat_1,k1_funct_2(c1_7__altcat_1,c2_7__altcat_1)) ),
    introduced(definition,[new_symbol(c4_7__altcat_1),file(altcat_1,c4_7__altcat_1)]),
    [interesting(0.8),axiom,file(altcat_1,c4_7__altcat_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(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(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(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(cc1_fraenkel,theorem,(
    ! [A] : 
      ( v1_fraenkel(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_relat_1(B)
            & v1_funct_1(B) ) ) ) ),
    file(fraenkel,cc1_fraenkel),
    [interesting(0.9),axiom,file(fraenkel,cc1_fraenkel)]).

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

fof(rc1_fraenkel,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_fraenkel(A) ) ),
    file(fraenkel,rc1_fraenkel),
    [interesting(0.9),axiom,file(fraenkel,rc1_fraenkel)]).

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_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_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(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(t8_boole,theorem,(
    ! [A,B] : 
      ~ ( v1_xboole_0(A)
        & A != B
        & v1_xboole_0(B) ) ),
    file(boole,t8_boole),
    [interesting(0.9),axiom,file(boole,t8_boole)]).

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

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

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

fof(dt_c1_7__altcat_1,assumption,(
    $true ),
    introduced(assumption,[file(altcat_1,c1_7__altcat_1)]),
    [interesting(0.8),axiom,file(altcat_1,c1_7__altcat_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(fc1_fraenkel,theorem,(
    ! [A,B] : v1_fraenkel(k1_funct_2(A,B)) ),
    file(fraenkel,fc1_fraenkel),
    [interesting(0.9),axiom,file(fraenkel,fc1_fraenkel)]).

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

fof(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(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(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(d1_xboole_0,definition,(
    ! [A] : 
      ( A = k1_xboole_0
    <=> ! [B] : ~ r2_hidden(B,A) ) ),
    file(xboole_0,d1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,d1_xboole_0)]).

fof(e3_7__altcat_1,plain,(
    ? [A] : r2_hidden(A,k1_funct_2(c1_7__altcat_1,c2_7__altcat_1)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__altcat_1,dt_c2_7__altcat_1,e1_7__altcat_1])],[rc3_funct_1,cc2_funct_1,rc1_funct_1,rc2_funct_1,rc4_funct_1,existence_m1_subset_1,dt_m1_subset_1,cc1_fraenkel,cc1_funct_1,cc1_relat_1,fc1_funct_2,rc1_fraenkel,rc1_relat_1,rc2_relat_1,rc3_relat_1,t2_subset,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_2,dt_k1_xboole_0,dt_c1_7__altcat_1,dt_c2_7__altcat_1,fc12_relat_1,fc1_fraenkel,fc2_funct_2,fc4_relat_1,t1_subset,t6_boole,t7_boole,e1_7__altcat_1,d1_xboole_0]),
    [interesting(0.8),file(altcat_1,e3_7__altcat_1),[file(altcat_1,e3_7__altcat_1)]]).

fof(dt_c4_7__altcat_1,plain,(
    $true ),
    inference(consider,[status(thm),assumptions([dt_c1_7__altcat_1,dt_c2_7__altcat_1,e1_7__altcat_1])],[dh_c4_7__altcat_1,e3_7__altcat_1]),
    [interesting(0.8),file(altcat_1,c4_7__altcat_1),[file(altcat_1,c4_7__altcat_1)]]).

fof(dh_c5_7__altcat_1,definition,
    ( ? [A] : r2_hidden(A,k1_funct_2(c2_7__altcat_1,c3_7__altcat_1))
   => r2_hidden(c5_7__altcat_1,k1_funct_2(c2_7__altcat_1,c3_7__altcat_1)) ),
    introduced(definition,[new_symbol(c5_7__altcat_1),file(altcat_1,c5_7__altcat_1)]),
    [interesting(0.8),axiom,file(altcat_1,c5_7__altcat_1)]).

fof(dt_c3_7__altcat_1,assumption,(
    $true ),
    introduced(assumption,[file(altcat_1,c3_7__altcat_1)]),
    [interesting(0.8),axiom,file(altcat_1,c3_7__altcat_1)]).

fof(e5_7__altcat_1,plain,(
    ? [A] : r2_hidden(A,k1_funct_2(c2_7__altcat_1,c3_7__altcat_1)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_7__altcat_1,dt_c3_7__altcat_1,e2_7__altcat_1])],[rc3_funct_1,cc2_funct_1,rc1_funct_1,rc2_funct_1,rc4_funct_1,existence_m1_subset_1,dt_m1_subset_1,cc1_fraenkel,cc1_funct_1,cc1_relat_1,fc1_funct_2,rc1_fraenkel,rc1_relat_1,rc2_relat_1,rc3_relat_1,t2_subset,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_2,dt_k1_xboole_0,dt_c2_7__altcat_1,dt_c3_7__altcat_1,fc12_relat_1,fc1_fraenkel,fc2_funct_2,fc4_relat_1,t1_subset,t6_boole,t7_boole,e2_7__altcat_1,d1_xboole_0]),
    [interesting(0.8),file(altcat_1,e5_7__altcat_1),[file(altcat_1,e5_7__altcat_1)]]).

fof(dt_c5_7__altcat_1,plain,(
    $true ),
    inference(consider,[status(thm),assumptions([dt_c2_7__altcat_1,dt_c3_7__altcat_1,e2_7__altcat_1])],[dh_c5_7__altcat_1,e5_7__altcat_1]),
    [interesting(0.8),file(altcat_1,c5_7__altcat_1),[file(altcat_1,c5_7__altcat_1)]]).

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(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(de_c6_7__altcat_1,definition,(
    c6_7__altcat_1 = c4_7__altcat_1 ),
    introduced(definition,[new_symbol(c6_7__altcat_1),file(altcat_1,c6_7__altcat_1)]),
    [interesting(0.8),axiom,file(altcat_1,c6_7__altcat_1)]).

fof(e4_7__altcat_1,plain,(
    r2_hidden(c4_7__altcat_1,k1_funct_2(c1_7__altcat_1,c2_7__altcat_1)) ),
    inference(consider,[status(thm),assumptions([dt_c1_7__altcat_1,dt_c2_7__altcat_1,e1_7__altcat_1])],[dh_c4_7__altcat_1,e3_7__altcat_1]),
    [interesting(0.8),file(altcat_1,e4_7__altcat_1),[file(altcat_1,e4_7__altcat_1)]]).

fof(t121_funct_2,theorem,(
    ! [A,B,C] : 
      ( r2_hidden(C,k1_funct_2(A,B))
     => ( v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m2_relset_1(C,A,B) ) ) ),
    file(funct_2,t121_funct_2),
    [interesting(0.9),axiom,file(funct_2,t121_funct_2)]).

fof(e7_7__altcat_1,plain,
    ( v1_funct_1(c4_7__altcat_1)
    & v1_funct_2(c4_7__altcat_1,c1_7__altcat_1,c2_7__altcat_1)
    & m2_relset_1(c4_7__altcat_1,c1_7__altcat_1,c2_7__altcat_1) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__altcat_1,dt_c2_7__altcat_1,e1_7__altcat_1])],[rc3_funct_1,rc3_relat_1,rc4_funct_1,reflexivity_r1_tarski,dt_k1_xboole_0,cc1_funct_2,cc1_tex_2,cc2_funct_1,fc12_relat_1,fc4_relat_1,rc1_funct_1,rc1_funct_2,rc1_relat_1,rc2_funct_1,rc2_relat_1,rc2_tex_2,rc3_tex_2,rc4_tex_2,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_altcat_1,cc1_fraenkel,cc1_funct_1,cc1_relat_1,cc1_relset_1,cc2_tex_2,cc5_funct_2,cc6_funct_2,fc1_funct_2,fc1_subset_1,fc4_subset_1,rc1_fraenkel,rc1_subset_1,rc2_subset_1,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,antisymmetry_r2_hidden,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_funct_2,dt_m2_relset_1,dt_c1_7__altcat_1,dt_c2_7__altcat_1,dt_c4_7__altcat_1,fc1_fraenkel,fc2_funct_2,t1_subset,t7_boole,e4_7__altcat_1,t121_funct_2]),
    [interesting(0.8),file(altcat_1,e7_7__altcat_1),[file(altcat_1,e7_7__altcat_1)]]).

fof(dt_c6_7__altcat_1,plain,
    ( v1_funct_1(c6_7__altcat_1)
    & v1_funct_2(c6_7__altcat_1,c1_7__altcat_1,c2_7__altcat_1)
    & m2_relset_1(c6_7__altcat_1,c1_7__altcat_1,c2_7__altcat_1) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__altcat_1,dt_c2_7__altcat_1,e1_7__altcat_1])],[rc3_relat_1,rc4_funct_1,antisymmetry_r2_hidden,dt_k1_xboole_0,cc1_funct_2,cc1_tex_2,fc12_relat_1,fc4_relat_1,rc2_tex_2,rc3_funct_1,rc3_tex_2,rc4_tex_2,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,cc1_funct_1,cc1_relat_1,cc2_funct_1,cc2_tex_2,cc5_funct_2,cc6_funct_2,fc4_subset_1,rc1_funct_1,rc1_funct_2,rc1_relat_1,rc1_subset_1,rc2_funct_1,rc2_relat_1,rc2_subset_1,t2_subset,t6_boole,t7_boole,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_relset_1,fc1_subset_1,t3_subset,existence_m2_relset_1,redefinition_m2_relset_1,dt_m2_relset_1,dt_c1_7__altcat_1,dt_c2_7__altcat_1,dt_c4_7__altcat_1,de_c6_7__altcat_1,e7_7__altcat_1]),
    [interesting(0.8),file(altcat_1,c6_7__altcat_1),[file(altcat_1,c6_7__altcat_1)]]).

fof(de_c7_7__altcat_1,definition,(
    c7_7__altcat_1 = c5_7__altcat_1 ),
    introduced(definition,[new_symbol(c7_7__altcat_1),file(altcat_1,c7_7__altcat_1)]),
    [interesting(0.8),axiom,file(altcat_1,c7_7__altcat_1)]).

fof(e6_7__altcat_1,plain,(
    r2_hidden(c5_7__altcat_1,k1_funct_2(c2_7__altcat_1,c3_7__altcat_1)) ),
    inference(consider,[status(thm),assumptions([dt_c2_7__altcat_1,dt_c3_7__altcat_1,e2_7__altcat_1])],[dh_c5_7__altcat_1,e5_7__altcat_1]),
    [interesting(0.8),file(altcat_1,e6_7__altcat_1),[file(altcat_1,e6_7__altcat_1)]]).

fof(e8_7__altcat_1,plain,
    ( v1_funct_1(c5_7__altcat_1)
    & v1_funct_2(c5_7__altcat_1,c2_7__altcat_1,c3_7__altcat_1)
    & m2_relset_1(c5_7__altcat_1,c2_7__altcat_1,c3_7__altcat_1) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_7__altcat_1,dt_c3_7__altcat_1,e2_7__altcat_1])],[rc3_funct_1,rc3_relat_1,rc4_funct_1,reflexivity_r1_tarski,dt_k1_xboole_0,cc1_funct_2,cc1_tex_2,cc2_funct_1,fc12_relat_1,fc4_relat_1,rc1_funct_1,rc1_funct_2,rc1_relat_1,rc2_funct_1,rc2_relat_1,rc2_tex_2,rc3_tex_2,rc4_tex_2,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_altcat_1,cc1_fraenkel,cc1_funct_1,cc1_relat_1,cc1_relset_1,cc2_tex_2,cc5_funct_2,cc6_funct_2,fc1_funct_2,fc1_subset_1,fc4_subset_1,rc1_fraenkel,rc1_subset_1,rc2_subset_1,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,antisymmetry_r2_hidden,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_funct_2,dt_m2_relset_1,dt_c2_7__altcat_1,dt_c3_7__altcat_1,dt_c5_7__altcat_1,fc1_fraenkel,fc2_funct_2,t1_subset,t7_boole,e6_7__altcat_1,t121_funct_2]),
    [interesting(0.8),file(altcat_1,e8_7__altcat_1),[file(altcat_1,e8_7__altcat_1)]]).

fof(dt_c7_7__altcat_1,plain,
    ( v1_funct_1(c7_7__altcat_1)
    & v1_funct_2(c7_7__altcat_1,c2_7__altcat_1,c3_7__altcat_1)
    & m2_relset_1(c7_7__altcat_1,c2_7__altcat_1,c3_7__altcat_1) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_7__altcat_1,dt_c3_7__altcat_1,e2_7__altcat_1])],[rc3_relat_1,rc4_funct_1,antisymmetry_r2_hidden,dt_k1_xboole_0,cc1_funct_2,cc1_tex_2,fc12_relat_1,fc4_relat_1,rc2_tex_2,rc3_funct_1,rc3_tex_2,rc4_tex_2,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,cc1_funct_1,cc1_relat_1,cc2_funct_1,cc2_tex_2,cc5_funct_2,cc6_funct_2,fc4_subset_1,rc1_funct_1,rc1_funct_2,rc1_relat_1,rc1_subset_1,rc2_funct_1,rc2_relat_1,rc2_subset_1,t2_subset,t6_boole,t7_boole,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_relset_1,fc1_subset_1,t3_subset,existence_m2_relset_1,redefinition_m2_relset_1,dt_m2_relset_1,dt_c2_7__altcat_1,dt_c3_7__altcat_1,dt_c5_7__altcat_1,de_c7_7__altcat_1,e8_7__altcat_1]),
    [interesting(0.8),file(altcat_1,c7_7__altcat_1),[file(altcat_1,c7_7__altcat_1)]]).

fof(t4_altcat_1,theorem,(
    ! [A,B,C,D] : 
      ( ( v1_relat_1(D)
        & v1_funct_1(D) )
     => ! [E] : 
          ( ( v1_relat_1(E)
            & v1_funct_1(E) )
         => ( ( r2_hidden(D,k1_funct_2(A,B))
              & r2_hidden(E,k1_funct_2(B,C)) )
           => r2_hidden(k5_relat_1(D,E),k1_funct_2(A,C)) ) ) ) ),
    file(altcat_1,t4_altcat_1),
    [interesting(0.9),axiom,file(altcat_1,t4_altcat_1)]).

fof(e9_7__altcat_1,plain,(
    r2_hidden(k5_relat_1(c6_7__altcat_1,c7_7__altcat_1),k1_funct_2(c1_7__altcat_1,c3_7__altcat_1)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__altcat_1,e1_7__altcat_1,dt_c2_7__altcat_1,dt_c3_7__altcat_1,e2_7__altcat_1])],[reflexivity_r1_tarski,cc1_funct_2,cc1_tex_2,rc2_tex_2,rc3_relat_1,rc3_tex_2,rc4_funct_1,rc4_tex_2,existence_m1_relset_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_altcat_1,cc1_relset_1,cc2_tex_2,cc5_funct_2,cc6_funct_2,fc12_relat_1,fc1_subset_1,fc4_relat_1,fc4_subset_1,rc1_funct_2,rc1_subset_1,rc2_subset_1,rc3_funct_1,t3_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_m1_subset_1,dt_m2_relset_1,cc1_fraenkel,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc10_relat_1,fc1_funct_2,fc9_relat_1,rc1_fraenkel,rc1_relat_1,rc2_funct_1,rc2_relat_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_2,dt_k5_relat_1,dt_c1_7__altcat_1,dt_c2_7__altcat_1,dt_c3_7__altcat_1,dt_c4_7__altcat_1,dt_c5_7__altcat_1,dt_c6_7__altcat_1,dt_c7_7__altcat_1,de_c6_7__altcat_1,de_c7_7__altcat_1,fc1_fraenkel,fc1_funct_1,fc2_funct_2,rc1_funct_1,t1_subset,t7_boole,e4_7__altcat_1,e6_7__altcat_1,t4_altcat_1]),
    [interesting(0.8),file(altcat_1,e9_7__altcat_1),[file(altcat_1,e9_7__altcat_1)]]).

fof(e10_7__altcat_1,plain,(
    k1_funct_2(c1_7__altcat_1,c3_7__altcat_1) != k1_xboole_0 ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__altcat_1,e1_7__altcat_1,dt_c2_7__altcat_1,dt_c3_7__altcat_1,e2_7__altcat_1])],[reflexivity_r1_tarski,cc1_funct_2,cc1_tex_2,rc2_tex_2,rc3_tex_2,rc4_tex_2,existence_m1_relset_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_altcat_1,cc1_relset_1,cc2_tex_2,cc5_funct_2,cc6_funct_2,fc1_subset_1,fc4_subset_1,rc1_funct_2,rc1_subset_1,rc2_subset_1,rc3_funct_1,t3_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_c2_7__altcat_1,dt_c4_7__altcat_1,dt_c5_7__altcat_1,cc1_fraenkel,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc10_relat_1,fc1_funct_1,fc1_funct_2,fc9_relat_1,rc1_fraenkel,rc1_funct_1,rc1_relat_1,rc2_funct_1,rc2_relat_1,rc3_relat_1,rc4_funct_1,t2_subset,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_2,dt_k1_xboole_0,dt_k5_relat_1,dt_c1_7__altcat_1,dt_c3_7__altcat_1,dt_c6_7__altcat_1,dt_c7_7__altcat_1,de_c6_7__altcat_1,de_c7_7__altcat_1,fc12_relat_1,fc1_fraenkel,fc2_funct_2,fc4_relat_1,t1_subset,t6_boole,t7_boole,e9_7__altcat_1]),
    [interesting(0.8),file(altcat_1,e10_7__altcat_1),[file(altcat_1,e10_7__altcat_1)]]).

fof(i3_7__altcat_1,theorem,(
    $true ),
    introduced(tautology,[file(altcat_1,i3_7__altcat_1)]),
    [interesting(0.8),trivial,file(altcat_1,i3_7__altcat_1)]).

fof(i2_7__altcat_1,plain,(
    k1_funct_2(c1_7__altcat_1,c3_7__altcat_1) != k1_xboole_0 ),
    inference(conclusion,[status(thm),assumptions([dt_c1_7__altcat_1,e1_7__altcat_1,dt_c2_7__altcat_1,dt_c3_7__altcat_1,e2_7__altcat_1])],[e10_7__altcat_1,i3_7__altcat_1]),
    [interesting(0.8),file(altcat_1,i2_7__altcat_1),[file(altcat_1,i2_7__altcat_1)]]).

fof(i1_7__altcat_1,plain,(
    ~ ( k1_funct_2(c1_7__altcat_1,c2_7__altcat_1) != k1_xboole_0
      & k1_funct_2(c2_7__altcat_1,c3_7__altcat_1) != k1_xboole_0
      & k1_funct_2(c1_7__altcat_1,c3_7__altcat_1) = k1_xboole_0 ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_7__altcat_1,dt_c2_7__altcat_1,dt_c3_7__altcat_1]),discharge_asm(discharge,[e1_7__altcat_1,e2_7__altcat_1])],[e1_7__altcat_1,e2_7__altcat_1,i2_7__altcat_1]),
    [interesting(0.8),file(altcat_1,i1_7__altcat_1),[file(altcat_1,i1_7__altcat_1)]]).

fof(i1_7_tmp__altcat_1,plain,(
    ~ ( k1_funct_2(c1_7__altcat_1,c2_7__altcat_1) != k1_xboole_0
      & k1_funct_2(c2_7__altcat_1,c3_7__altcat_1) != k1_xboole_0
      & k1_funct_2(c1_7__altcat_1,c3_7__altcat_1) = k1_xboole_0 ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_7__altcat_1,dt_c2_7__altcat_1,dt_c3_7__altcat_1])],[dt_c1_7__altcat_1,dt_c2_7__altcat_1,dt_c3_7__altcat_1,i1_7__altcat_1]),
    [interesting(1),t5_altcat_1]).

fof(t5_altcat_1,theorem,(
    ! [A,B,C] : 
      ~ ( k1_funct_2(A,B) != k1_xboole_0
        & k1_funct_2(B,C) != k1_xboole_0
        & k1_funct_2(A,C) = k1_xboole_0 ) ),
    inference(let,[status(thm),assumptions([])],[i1_7_tmp__altcat_1,dh_c1_7__altcat_1,dh_c2_7__altcat_1,dh_c3_7__altcat_1]),
    [interesting(1),file(altcat_1,t5_altcat_1),[file(altcat_1,t5_altcat_1)]]).