% Mizar ND problem: t3_altcat_1,altcat_1,62,23 
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(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(fc2_altcat_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( ~ v1_xboole_0(k1_tarski(A))
        & v1_finset_1(k1_tarski(A))
        & v1_fraenkel(k1_tarski(A))
        & v1_realset1(k1_tarski(A)) ) ) ),
    file(altcat_1,fc2_altcat_1),
    [interesting(0.9),axiom,file(altcat_1,fc2_altcat_1)]).

fof(fc2_fraenkel,theorem,(
    ! [A,B] : 
      ( ( v1_finset_1(A)
        & v1_finset_1(B) )
     => ( v1_finset_1(k1_funct_2(A,B))
        & v1_fraenkel(k1_funct_2(A,B)) ) ) ),
    file(fraenkel,fc2_fraenkel),
    [interesting(0.9),axiom,file(fraenkel,fc2_fraenkel)]).

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_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_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_tex_2,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_realset1(A) ) ),
    file(tex_2,rc1_tex_2),
    [interesting(0.9),axiom,file(tex_2,rc1_tex_2)]).

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

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

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

fof(dt_k1_tarski,axiom,(
    $true ),
    file(tarski,k1_tarski),
    [interesting(0.9),axiom,file(tarski,k1_tarski)]).

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_k6_relat_1,axiom,(
    ! [A] : v1_relat_1(k6_relat_1(A)) ),
    file(relat_1,k6_relat_1),
    [interesting(0.9),axiom,file(relat_1,k6_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(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(fc1_tex_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(k1_tarski(A))
      & v1_realset1(k1_tarski(A))
      & v1_finset_1(k1_tarski(A)) ) ),
    file(tex_2,fc1_tex_2),
    [interesting(0.9),axiom,file(tex_2,fc1_tex_2)]).

fof(fc2_funct_1,theorem,(
    ! [A] : 
      ( v1_relat_1(k6_relat_1(A))
      & v1_funct_1(k6_relat_1(A)) ) ),
    file(funct_1,fc2_funct_1),
    [interesting(0.9),axiom,file(funct_1,fc2_funct_1)]).

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(fc2_subset_1,theorem,(
    ! [A] : ~ v1_xboole_0(k1_tarski(A)) ),
    file(subset_1,fc2_subset_1),
    [interesting(0.9),axiom,file(subset_1,fc2_subset_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(d3_tarski,definition,(
    ! [A,B] : 
      ( r1_tarski(A,B)
    <=> ! [C] : 
          ( r2_hidden(C,A)
         => r2_hidden(C,B) ) ) ),
    file(tarski,d3_tarski),
    [interesting(0.9),axiom,file(tarski,d3_tarski)]).

fof(d10_xboole_0,definition,(
    ! [A,B] : 
      ( A = B
    <=> ( r1_tarski(A,B)
        & r1_tarski(B,A) ) ) ),
    file(xboole_0,d10_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,d10_xboole_0)]).

fof(dh_c1_5_1__altcat_1,definition,
    ( ( r2_hidden(c1_5_1__altcat_1,k1_funct_2(k1_xboole_0,k1_xboole_0))
     => r2_hidden(c1_5_1__altcat_1,k1_tarski(k6_relat_1(k1_xboole_0))) )
   => ! [A] : 
        ( r2_hidden(A,k1_funct_2(k1_xboole_0,k1_xboole_0))
       => r2_hidden(A,k1_tarski(k6_relat_1(k1_xboole_0))) ) ),
    introduced(definition,[new_symbol(c1_5_1__altcat_1),file(altcat_1,c1_5_1__altcat_1)]),
    [interesting(0.65),axiom,file(altcat_1,c1_5_1__altcat_1)]).

fof(e1_5_1__altcat_1,assumption,(
    r2_hidden(c1_5_1__altcat_1,k1_funct_2(k1_xboole_0,k1_xboole_0)) ),
    introduced(assumption,[file(altcat_1,e1_5_1__altcat_1)]),
    [interesting(0.65),axiom,file(altcat_1,e1_5_1__altcat_1)]).

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(cc3_tex_2,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_realset1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_tex_2(B,k1_zfmisc_1(A))
           => ( v1_xboole_0(B)
              & v1_membered(B)
              & v2_membered(B)
              & v3_membered(B)
              & v4_membered(B)
              & v5_membered(B)
              & v1_tex_2(B,k1_zfmisc_1(A)) ) ) ) ) ),
    file(tex_2,cc3_tex_2),
    [interesting(0.9),axiom,file(tex_2,cc3_tex_2)]).

fof(cc5_tex_2,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_realset1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( ( ~ v1_xboole_0(B)
              & ~ v1_tex_2(B,k1_zfmisc_1(A)) )
           => ( ~ v1_xboole_0(B)
              & v1_realset1(B)
              & ~ v1_tex_2(B,k1_zfmisc_1(A)) ) ) ) ) ),
    file(tex_2,cc5_tex_2),
    [interesting(0.9),axiom,file(tex_2,cc5_tex_2)]).

fof(cc7_tex_2,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_realset1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( ( ~ v1_xboole_0(B)
              & ~ v1_tex_2(B,k1_zfmisc_1(A)) )
           => ( ~ v1_xboole_0(B)
              & ~ v1_realset1(B) ) ) ) ) ),
    file(tex_2,cc7_tex_2),
    [interesting(0.9),axiom,file(tex_2,cc7_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(rc6_tex_2,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_realset1(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & v1_realset1(B)
          & v1_tex_2(B,k1_zfmisc_1(A)) ) ) ),
    file(tex_2,rc6_tex_2),
    [interesting(0.9),axiom,file(tex_2,rc6_tex_2)]).

fof(rc7_tex_2,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_realset1(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & ~ v1_realset1(B)
          & ~ v1_tex_2(B,k1_zfmisc_1(A)) ) ) ),
    file(tex_2,rc7_tex_2),
    [interesting(0.9),axiom,file(tex_2,rc7_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_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_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(cc4_tex_2,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_realset1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( ~ v1_xboole_0(B)
           => ( ~ v1_xboole_0(B)
              & ~ v1_tex_2(B,k1_zfmisc_1(A)) ) ) ) ) ),
    file(tex_2,cc4_tex_2),
    [interesting(0.9),axiom,file(tex_2,cc4_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(cc6_tex_2,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_realset1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( ( ~ v1_xboole_0(B)
              & v1_realset1(B) )
           => ( ~ v1_xboole_0(B)
              & v1_tex_2(B,k1_zfmisc_1(A)) ) ) ) ) ),
    file(tex_2,cc6_tex_2),
    [interesting(0.9),axiom,file(tex_2,cc6_tex_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(rc5_tex_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & v1_realset1(B) ) ) ),
    file(tex_2,rc5_tex_2),
    [interesting(0.9),axiom,file(tex_2,rc5_tex_2)]).

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(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(dt_c1_5_1__altcat_1,assumption,(
    $true ),
    introduced(assumption,[file(altcat_1,c1_5_1__altcat_1)]),
    [interesting(0.65),axiom,file(altcat_1,c1_5_1__altcat_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(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(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_5_1__altcat_1,definition,(
    c2_5_1__altcat_1 = c1_5_1__altcat_1 ),
    introduced(definition,[new_symbol(c2_5_1__altcat_1),file(altcat_1,c2_5_1__altcat_1)]),
    [interesting(0.65),axiom,file(altcat_1,c2_5_1__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(e2_5_1__altcat_1,plain,
    ( v1_funct_1(c1_5_1__altcat_1)
    & v1_funct_2(c1_5_1__altcat_1,k1_xboole_0,k1_xboole_0)
    & m2_relset_1(c1_5_1__altcat_1,k1_xboole_0,k1_xboole_0) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5_1__altcat_1,e1_5_1__altcat_1])],[reflexivity_r1_tarski,cc1_funct_2,cc1_tex_2,rc2_tex_2,rc3_funct_1,rc3_tex_2,rc4_tex_2,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_funct_1,cc2_tex_2,cc5_funct_2,cc6_funct_2,fc1_funct_2,fc1_subset_1,fc4_subset_1,rc1_fraenkel,rc1_funct_1,rc1_funct_2,rc1_relat_1,rc1_subset_1,rc2_funct_1,rc2_relat_1,rc2_subset_1,rc3_relat_1,rc4_funct_1,t2_subset,t3_subset,t4_subset,t5_subset,t8_boole,antisymmetry_r2_hidden,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_funct_2,dt_k1_xboole_0,dt_m2_relset_1,dt_c1_5_1__altcat_1,fc12_relat_1,fc1_fraenkel,fc2_funct_2,fc4_relat_1,t1_subset,t6_boole,t7_boole,e1_5_1__altcat_1,t121_funct_2]),
    [interesting(0.65),file(altcat_1,e2_5_1__altcat_1),[file(altcat_1,e2_5_1__altcat_1)]]).

fof(dt_c2_5_1__altcat_1,plain,
    ( v1_funct_1(c2_5_1__altcat_1)
    & v1_funct_2(c2_5_1__altcat_1,k1_xboole_0,k1_xboole_0)
    & m2_relset_1(c2_5_1__altcat_1,k1_xboole_0,k1_xboole_0) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5_1__altcat_1,e1_5_1__altcat_1])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,cc1_funct_2,cc1_tex_2,rc2_tex_2,rc3_funct_1,rc3_tex_2,rc4_tex_2,t1_subset,t4_subset,t5_subset,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,cc2_tex_2,cc5_funct_2,cc6_funct_2,fc1_subset_1,fc4_subset_1,rc1_funct_1,rc1_funct_2,rc1_relat_1,rc1_subset_1,rc2_funct_1,rc2_relat_1,rc2_subset_1,rc3_relat_1,rc4_funct_1,t2_subset,t3_subset,t7_boole,t8_boole,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_m2_relset_1,dt_c1_5_1__altcat_1,fc12_relat_1,fc4_relat_1,t6_boole,de_c2_5_1__altcat_1,e2_5_1__altcat_1]),
    [interesting(0.65),file(altcat_1,c2_5_1__altcat_1),[file(altcat_1,c2_5_1__altcat_1)]]).

fof(commutativity_k2_tarski,theorem,(
    ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ),
    file(tarski,k2_tarski),
    [interesting(0.9),axiom,file(tarski,k2_tarski)]).

fof(dt_k2_tarski,axiom,(
    $true ),
    file(tarski,k2_tarski),
    [interesting(0.9),axiom,file(tarski,k2_tarski)]).

fof(fc3_subset_1,theorem,(
    ! [A,B] : ~ v1_xboole_0(k2_tarski(A,B)) ),
    file(subset_1,fc3_subset_1),
    [interesting(0.9),axiom,file(subset_1,fc3_subset_1)]).

fof(dt_k4_tarski,axiom,(
    $true ),
    file(tarski,k4_tarski),
    [interesting(0.9),axiom,file(tarski,k4_tarski)]).

fof(d5_tarski,definition,(
    ! [A,B] : k4_tarski(A,B) = k2_tarski(k2_tarski(A,B),k1_tarski(A)) ),
    file(tarski,d5_tarski),
    [interesting(0.9),axiom,file(tarski,d5_tarski)]).

fof(dh_c1_5_1_1__altcat_1,definition,
    ( ! [A] : 
        ( ( r2_hidden(k4_tarski(c1_5_1_1__altcat_1,A),c2_5_1__altcat_1)
         => ( r2_hidden(c1_5_1_1__altcat_1,k1_xboole_0)
            & c1_5_1_1__altcat_1 = A ) )
        & ( ( r2_hidden(c1_5_1_1__altcat_1,k1_xboole_0)
            & c1_5_1_1__altcat_1 = A )
         => r2_hidden(k4_tarski(c1_5_1_1__altcat_1,A),c2_5_1__altcat_1) ) )
   => ! [B,C] : 
        ( ( r2_hidden(k4_tarski(B,C),c2_5_1__altcat_1)
         => ( r2_hidden(B,k1_xboole_0)
            & B = C ) )
        & ( ( r2_hidden(B,k1_xboole_0)
            & B = C )
         => r2_hidden(k4_tarski(B,C),c2_5_1__altcat_1) ) ) ),
    introduced(definition,[new_symbol(c1_5_1_1__altcat_1),file(altcat_1,c1_5_1_1__altcat_1)]),
    [interesting(0.5),axiom,file(altcat_1,c1_5_1_1__altcat_1)]).

fof(dh_c2_5_1_1__altcat_1,definition,
    ( ( ( r2_hidden(k4_tarski(c1_5_1_1__altcat_1,c2_5_1_1__altcat_1),c2_5_1__altcat_1)
       => ( r2_hidden(c1_5_1_1__altcat_1,k1_xboole_0)
          & c1_5_1_1__altcat_1 = c2_5_1_1__altcat_1 ) )
      & ( ( r2_hidden(c1_5_1_1__altcat_1,k1_xboole_0)
          & c1_5_1_1__altcat_1 = c2_5_1_1__altcat_1 )
       => r2_hidden(k4_tarski(c1_5_1_1__altcat_1,c2_5_1_1__altcat_1),c2_5_1__altcat_1) ) )
   => ! [A] : 
        ( ( r2_hidden(k4_tarski(c1_5_1_1__altcat_1,A),c2_5_1__altcat_1)
         => ( r2_hidden(c1_5_1_1__altcat_1,k1_xboole_0)
            & c1_5_1_1__altcat_1 = A ) )
        & ( ( r2_hidden(c1_5_1_1__altcat_1,k1_xboole_0)
            & c1_5_1_1__altcat_1 = A )
         => r2_hidden(k4_tarski(c1_5_1_1__altcat_1,A),c2_5_1__altcat_1) ) ) ),
    introduced(definition,[new_symbol(c2_5_1_1__altcat_1),file(altcat_1,c2_5_1_1__altcat_1)]),
    [interesting(0.5),axiom,file(altcat_1,c2_5_1_1__altcat_1)]).

fof(e1_5_1_1_1__altcat_1,assumption,(
    r2_hidden(k4_tarski(c1_5_1_1__altcat_1,c2_5_1_1__altcat_1),c2_5_1__altcat_1) ),
    introduced(assumption,[file(altcat_1,e1_5_1_1_1__altcat_1)]),
    [interesting(0.35),axiom,file(altcat_1,e1_5_1_1_1__altcat_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_k1_relat_1,axiom,(
    $true ),
    file(relat_1,k1_relat_1),
    [interesting(0.9),axiom,file(relat_1,k1_relat_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(dt_c1_5_1_1__altcat_1,assumption,(
    $true ),
    introduced(assumption,[file(altcat_1,c1_5_1_1__altcat_1)]),
    [interesting(0.5),axiom,file(altcat_1,c1_5_1_1__altcat_1)]).

fof(dt_c2_5_1_1__altcat_1,assumption,(
    $true ),
    introduced(assumption,[file(altcat_1,c2_5_1_1__altcat_1)]),
    [interesting(0.5),axiom,file(altcat_1,c2_5_1_1__altcat_1)]).

fof(d4_relat_1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( B = k1_relat_1(A)
        <=> ! [C] : 
              ( r2_hidden(C,B)
            <=> ? [D] : r2_hidden(k4_tarski(C,D),A) ) ) ) ),
    file(relat_1,d4_relat_1),
    [interesting(0.9),axiom,file(relat_1,d4_relat_1)]).

fof(e2_5_1_1_1__altcat_1,plain,(
    r2_hidden(c1_5_1_1__altcat_1,k1_relat_1(c2_5_1__altcat_1)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5_1_1__altcat_1,dt_c1_5_1__altcat_1,e1_5_1__altcat_1,dt_c2_5_1_1__altcat_1,e1_5_1_1_1__altcat_1])],[reflexivity_r1_tarski,cc1_funct_2,cc1_tex_2,cc3_tex_2,cc5_tex_2,cc7_tex_2,rc2_tex_2,rc3_tex_2,rc4_tex_2,rc6_tex_2,rc7_tex_2,existence_m1_relset_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_altcat_1,cc1_fraenkel,cc1_relset_1,cc2_tex_2,cc4_tex_2,cc5_funct_2,cc6_funct_2,cc6_tex_2,fc1_subset_1,fc4_subset_1,rc1_fraenkel,rc1_funct_2,rc1_subset_1,rc1_tex_2,rc2_subset_1,rc3_funct_1,rc3_relat_1,rc4_funct_1,rc5_tex_2,t3_subset,t4_subset,t5_subset,commutativity_k2_tarski,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_tarski,dt_k1_xboole_0,dt_k2_tarski,dt_m1_subset_1,dt_m2_relset_1,dt_c1_5_1__altcat_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc12_relat_1,fc1_tex_2,fc2_altcat_1,fc2_subset_1,fc3_subset_1,fc4_relat_1,fc5_relat_1,fc7_relat_1,rc1_funct_1,rc1_relat_1,rc2_funct_1,rc2_relat_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_relat_1,dt_k4_tarski,dt_c1_5_1_1__altcat_1,dt_c2_5_1__altcat_1,dt_c2_5_1_1__altcat_1,de_c2_5_1__altcat_1,t1_subset,t7_boole,d5_tarski,e1_5_1_1_1__altcat_1,d4_relat_1]),
    [interesting(0.35),file(altcat_1,e2_5_1_1_1__altcat_1),[file(altcat_1,e2_5_1_1_1__altcat_1)]]).

fof(d1_funct_2,definition,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => ( ( ( B = k1_xboole_0
           => A = k1_xboole_0 )
         => ( v1_funct_2(C,A,B)
          <=> A = k4_relset_1(A,B,C) ) )
        & ( B = k1_xboole_0
         => ( A = k1_xboole_0
            | ( v1_funct_2(C,A,B)
            <=> C = k1_xboole_0 ) ) ) ) ) ),
    file(funct_2,d1_funct_2),
    [interesting(0.9),axiom,file(funct_2,d1_funct_2)]).

fof(e3_5_1_1_1__altcat_1,plain,(
    r2_hidden(c1_5_1_1__altcat_1,k1_xboole_0) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5_1_1__altcat_1,dt_c1_5_1__altcat_1,e1_5_1__altcat_1,dt_c2_5_1_1__altcat_1,e1_5_1_1_1__altcat_1])],[reflexivity_r1_tarski,cc1_funct_2,cc1_tex_2,rc2_tex_2,rc3_funct_1,rc3_tex_2,rc4_tex_2,existence_m1_relset_1,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_m1_relset_1,dt_m1_subset_1,dt_c1_5_1__altcat_1,cc1_funct_1,cc1_relat_1,cc1_relset_1,cc2_funct_1,cc2_tex_2,cc5_funct_2,cc6_funct_2,fc1_subset_1,fc4_subset_1,fc5_relat_1,fc7_relat_1,rc1_funct_1,rc1_funct_2,rc1_relat_1,rc1_subset_1,rc2_funct_1,rc2_relat_1,rc2_subset_1,rc3_relat_1,rc4_funct_1,t2_subset,t3_subset,t4_subset,t5_subset,t8_boole,antisymmetry_r2_hidden,existence_m2_relset_1,redefinition_k4_relset_1,redefinition_m2_relset_1,dt_k1_relat_1,dt_k1_xboole_0,dt_k4_relset_1,dt_m2_relset_1,dt_c1_5_1_1__altcat_1,dt_c2_5_1__altcat_1,de_c2_5_1__altcat_1,fc12_relat_1,fc4_relat_1,t1_subset,t6_boole,t7_boole,e2_5_1_1_1__altcat_1,d1_funct_2]),
    [interesting(0.35),file(altcat_1,e3_5_1_1_1__altcat_1),[file(altcat_1,e3_5_1_1_1__altcat_1)]]).

fof(e4_5_1_1_1__altcat_1,plain,(
    c1_5_1_1__altcat_1 = c2_5_1_1__altcat_1 ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5_1_1__altcat_1,dt_c1_5_1__altcat_1,e1_5_1__altcat_1,dt_c2_5_1_1__altcat_1,e1_5_1_1_1__altcat_1])],[reflexivity_r1_tarski,cc1_funct_2,cc1_tex_2,rc2_tex_2,rc3_funct_1,rc3_tex_2,rc4_tex_2,existence_m1_relset_1,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_m1_relset_1,dt_m1_subset_1,dt_c1_5_1__altcat_1,cc1_funct_1,cc1_relat_1,cc1_relset_1,cc2_funct_1,cc2_tex_2,cc5_funct_2,cc6_funct_2,fc1_subset_1,fc4_subset_1,fc5_relat_1,fc7_relat_1,rc1_funct_1,rc1_funct_2,rc1_relat_1,rc1_subset_1,rc2_funct_1,rc2_relat_1,rc2_subset_1,rc3_relat_1,rc4_funct_1,t2_subset,t3_subset,t4_subset,t5_subset,t8_boole,antisymmetry_r2_hidden,existence_m2_relset_1,redefinition_k4_relset_1,redefinition_m2_relset_1,dt_k1_relat_1,dt_k1_xboole_0,dt_k4_relset_1,dt_m2_relset_1,dt_c1_5_1_1__altcat_1,dt_c2_5_1__altcat_1,dt_c2_5_1_1__altcat_1,de_c2_5_1__altcat_1,fc12_relat_1,fc4_relat_1,t1_subset,t6_boole,t7_boole,e2_5_1_1_1__altcat_1,d1_funct_2]),
    [interesting(0.35),file(altcat_1,e4_5_1_1_1__altcat_1),[file(altcat_1,e4_5_1_1_1__altcat_1)]]).

fof(i3_5_1_1_1__altcat_1,theorem,(
    $true ),
    introduced(tautology,[file(altcat_1,i3_5_1_1_1__altcat_1)]),
    [interesting(0.35),trivial,file(altcat_1,i3_5_1_1_1__altcat_1)]).

fof(i2_5_1_1_1__altcat_1,plain,(
    c1_5_1_1__altcat_1 = c2_5_1_1__altcat_1 ),
    inference(conclusion,[status(thm),assumptions([dt_c1_5_1_1__altcat_1,dt_c1_5_1__altcat_1,e1_5_1__altcat_1,dt_c2_5_1_1__altcat_1,e1_5_1_1_1__altcat_1])],[e4_5_1_1_1__altcat_1,i3_5_1_1_1__altcat_1]),
    [interesting(0.35),file(altcat_1,i2_5_1_1_1__altcat_1),[file(altcat_1,i2_5_1_1_1__altcat_1)]]).

fof(i1_5_1_1_1__altcat_1,plain,
    ( r2_hidden(c1_5_1_1__altcat_1,k1_xboole_0)
    & c1_5_1_1__altcat_1 = c2_5_1_1__altcat_1 ),
    inference(conclusion,[status(thm),assumptions([dt_c1_5_1_1__altcat_1,dt_c1_5_1__altcat_1,e1_5_1__altcat_1,dt_c2_5_1_1__altcat_1,e1_5_1_1_1__altcat_1])],[e3_5_1_1_1__altcat_1,i2_5_1_1_1__altcat_1]),
    [interesting(0.35),file(altcat_1,i1_5_1_1_1__altcat_1),[file(altcat_1,i1_5_1_1_1__altcat_1)]]).

fof(e1_5_1_1__altcat_1,plain,
    ( r2_hidden(k4_tarski(c1_5_1_1__altcat_1,c2_5_1_1__altcat_1),c2_5_1__altcat_1)
   => ( r2_hidden(c1_5_1_1__altcat_1,k1_xboole_0)
      & c1_5_1_1__altcat_1 = c2_5_1_1__altcat_1 ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_5_1_1__altcat_1,dt_c1_5_1__altcat_1,e1_5_1__altcat_1,dt_c2_5_1_1__altcat_1]),discharge_asm(discharge,[e1_5_1_1_1__altcat_1])],[e1_5_1_1_1__altcat_1,i1_5_1_1_1__altcat_1]),
    [interesting(0.5),file(altcat_1,e1_5_1_1__altcat_1),[file(altcat_1,e1_5_1_1__altcat_1)]]).

fof(e2_5_1_1__altcat_1,plain,
    ( ( r2_hidden(c1_5_1_1__altcat_1,k1_xboole_0)
      & c1_5_1_1__altcat_1 = c2_5_1_1__altcat_1 )
   => r2_hidden(k4_tarski(c1_5_1_1__altcat_1,c2_5_1_1__altcat_1),c2_5_1__altcat_1) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5_1_1__altcat_1,dt_c1_5_1__altcat_1,e1_5_1__altcat_1,dt_c2_5_1_1__altcat_1])],[reflexivity_r1_tarski,cc1_funct_2,cc1_tex_2,cc3_tex_2,cc5_tex_2,cc7_tex_2,rc2_tex_2,rc3_tex_2,rc4_tex_2,rc6_tex_2,rc7_tex_2,existence_m1_relset_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_altcat_1,cc1_fraenkel,cc1_relset_1,cc2_tex_2,cc4_tex_2,cc5_funct_2,cc6_funct_2,cc6_tex_2,fc1_subset_1,fc4_subset_1,rc1_fraenkel,rc1_funct_2,rc1_subset_1,rc1_tex_2,rc2_subset_1,rc3_funct_1,rc5_tex_2,t3_subset,t4_subset,t5_subset,commutativity_k2_tarski,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_tarski,dt_k2_tarski,dt_m1_subset_1,dt_m2_relset_1,dt_c1_5_1__altcat_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc1_tex_2,fc2_altcat_1,fc2_subset_1,fc3_subset_1,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_xboole_0,dt_k4_tarski,dt_c1_5_1_1__altcat_1,dt_c2_5_1__altcat_1,dt_c2_5_1_1__altcat_1,de_c2_5_1__altcat_1,fc12_relat_1,fc4_relat_1,t1_subset,t6_boole,t7_boole,d5_tarski]),
    [interesting(0.5),file(altcat_1,e2_5_1_1__altcat_1),[file(altcat_1,e2_5_1_1__altcat_1)]]).

fof(i3_5_1_1__altcat_1,theorem,(
    $true ),
    introduced(tautology,[file(altcat_1,i3_5_1_1__altcat_1)]),
    [interesting(0.5),trivial,file(altcat_1,i3_5_1_1__altcat_1)]).

fof(i2_5_1_1__altcat_1,plain,
    ( ( r2_hidden(c1_5_1_1__altcat_1,k1_xboole_0)
      & c1_5_1_1__altcat_1 = c2_5_1_1__altcat_1 )
   => r2_hidden(k4_tarski(c1_5_1_1__altcat_1,c2_5_1_1__altcat_1),c2_5_1__altcat_1) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_5_1_1__altcat_1,dt_c1_5_1__altcat_1,e1_5_1__altcat_1,dt_c2_5_1_1__altcat_1])],[e2_5_1_1__altcat_1,i3_5_1_1__altcat_1]),
    [interesting(0.5),file(altcat_1,i2_5_1_1__altcat_1),[file(altcat_1,i2_5_1_1__altcat_1)]]).

fof(i1_5_1_1__altcat_1,plain,
    ( ( r2_hidden(k4_tarski(c1_5_1_1__altcat_1,c2_5_1_1__altcat_1),c2_5_1__altcat_1)
     => ( r2_hidden(c1_5_1_1__altcat_1,k1_xboole_0)
        & c1_5_1_1__altcat_1 = c2_5_1_1__altcat_1 ) )
    & ( ( r2_hidden(c1_5_1_1__altcat_1,k1_xboole_0)
        & c1_5_1_1__altcat_1 = c2_5_1_1__altcat_1 )
     => r2_hidden(k4_tarski(c1_5_1_1__altcat_1,c2_5_1_1__altcat_1),c2_5_1__altcat_1) ) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_5_1_1__altcat_1,dt_c1_5_1__altcat_1,e1_5_1__altcat_1,dt_c2_5_1_1__altcat_1])],[e1_5_1_1__altcat_1,i2_5_1_1__altcat_1]),
    [interesting(0.5),file(altcat_1,i1_5_1_1__altcat_1),[file(altcat_1,i1_5_1_1__altcat_1)]]).

fof(i1_5_1_1_tmp__altcat_1,plain,
    ( ( r2_hidden(k4_tarski(c1_5_1_1__altcat_1,c2_5_1_1__altcat_1),c2_5_1__altcat_1)
     => ( r2_hidden(c1_5_1_1__altcat_1,k1_xboole_0)
        & c1_5_1_1__altcat_1 = c2_5_1_1__altcat_1 ) )
    & ( ( r2_hidden(c1_5_1_1__altcat_1,k1_xboole_0)
        & c1_5_1_1__altcat_1 = c2_5_1_1__altcat_1 )
     => r2_hidden(k4_tarski(c1_5_1_1__altcat_1,c2_5_1_1__altcat_1),c2_5_1__altcat_1) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_5_1__altcat_1,e1_5_1__altcat_1]),discharge_asm(discharge,[dt_c1_5_1_1__altcat_1,dt_c2_5_1_1__altcat_1])],[dt_c1_5_1_1__altcat_1,dt_c2_5_1_1__altcat_1,i1_5_1_1__altcat_1]),
    [interesting(0.65),e3_5_1__altcat_1]).

fof(e3_5_1__altcat_1,plain,(
    ! [A,B] : 
      ( ( r2_hidden(k4_tarski(A,B),c2_5_1__altcat_1)
       => ( r2_hidden(A,k1_xboole_0)
          & A = B ) )
      & ( ( r2_hidden(A,k1_xboole_0)
          & A = B )
       => r2_hidden(k4_tarski(A,B),c2_5_1__altcat_1) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_5_1__altcat_1,e1_5_1__altcat_1])],[i1_5_1_1_tmp__altcat_1,dh_c1_5_1_1__altcat_1,dh_c2_5_1_1__altcat_1]),
    [interesting(0.65),file(altcat_1,e3_5_1__altcat_1),[file(altcat_1,e3_5_1__altcat_1)]]).

fof(d10_relat_1,definition,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ( B = k6_relat_1(A)
      <=> ! [C,D] : 
            ( r2_hidden(k4_tarski(C,D),B)
          <=> ( r2_hidden(C,A)
              & C = D ) ) ) ) ),
    file(relat_1,d10_relat_1),
    [interesting(0.9),axiom,file(relat_1,d10_relat_1)]).

fof(e4_5_1__altcat_1,plain,(
    c2_5_1__altcat_1 = k6_relat_1(k1_xboole_0) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5_1__altcat_1,e1_5_1__altcat_1])],[reflexivity_r1_tarski,cc1_funct_2,cc1_tex_2,cc3_tex_2,cc5_tex_2,cc7_tex_2,rc2_tex_2,rc3_tex_2,rc4_tex_2,rc6_tex_2,rc7_tex_2,existence_m1_relset_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_altcat_1,cc1_fraenkel,cc1_relset_1,cc2_tex_2,cc4_tex_2,cc5_funct_2,cc6_funct_2,cc6_tex_2,fc1_subset_1,fc4_subset_1,rc1_fraenkel,rc1_funct_2,rc1_subset_1,rc1_tex_2,rc2_subset_1,rc3_funct_1,rc5_tex_2,t3_subset,t4_subset,t5_subset,commutativity_k2_tarski,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_tarski,dt_k2_tarski,dt_m1_subset_1,dt_m2_relset_1,dt_c1_5_1__altcat_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc1_tex_2,fc2_altcat_1,fc2_subset_1,fc3_subset_1,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_xboole_0,dt_k4_tarski,dt_k6_relat_1,dt_c2_5_1__altcat_1,de_c2_5_1__altcat_1,fc12_relat_1,fc2_funct_1,fc4_relat_1,t1_subset,t6_boole,t7_boole,d5_tarski,e3_5_1__altcat_1,d10_relat_1]),
    [interesting(0.65),file(altcat_1,e4_5_1__altcat_1),[file(altcat_1,e4_5_1__altcat_1)]]).

fof(d1_tarski,definition,(
    ! [A,B] : 
      ( B = k1_tarski(A)
    <=> ! [C] : 
          ( r2_hidden(C,B)
        <=> C = A ) ) ),
    file(tarski,d1_tarski),
    [interesting(0.9),axiom,file(tarski,d1_tarski)]).

fof(e5_5_1__altcat_1,plain,(
    r2_hidden(c1_5_1__altcat_1,k1_tarski(k6_relat_1(k1_xboole_0))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5_1__altcat_1,e1_5_1__altcat_1])],[reflexivity_r1_tarski,cc1_funct_2,cc1_tex_2,cc3_tex_2,cc5_tex_2,cc7_tex_2,rc2_tex_2,rc3_tex_2,rc4_tex_2,rc6_tex_2,rc7_tex_2,existence_m1_relset_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_altcat_1,cc1_fraenkel,cc1_relset_1,cc2_tex_2,cc4_tex_2,cc5_funct_2,cc6_funct_2,cc6_tex_2,fc1_subset_1,fc4_subset_1,rc1_fraenkel,rc1_funct_2,rc1_subset_1,rc2_subset_1,rc3_funct_1,rc5_tex_2,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_funct_1,cc1_relat_1,cc2_funct_1,fc2_altcat_1,rc1_funct_1,rc1_relat_1,rc1_tex_2,rc2_funct_1,rc2_relat_1,rc3_relat_1,rc4_funct_1,t2_subset,t8_boole,antisymmetry_r2_hidden,dt_k1_tarski,dt_k1_xboole_0,dt_k6_relat_1,dt_c1_5_1__altcat_1,dt_c2_5_1__altcat_1,de_c2_5_1__altcat_1,fc12_relat_1,fc1_tex_2,fc2_funct_1,fc2_subset_1,fc4_relat_1,t1_subset,t6_boole,t7_boole,e4_5_1__altcat_1,d1_tarski]),
    [interesting(0.65),file(altcat_1,e5_5_1__altcat_1),[file(altcat_1,e5_5_1__altcat_1)]]).

fof(i3_5_1__altcat_1,theorem,(
    $true ),
    introduced(tautology,[file(altcat_1,i3_5_1__altcat_1)]),
    [interesting(0.65),trivial,file(altcat_1,i3_5_1__altcat_1)]).

fof(i2_5_1__altcat_1,plain,(
    r2_hidden(c1_5_1__altcat_1,k1_tarski(k6_relat_1(k1_xboole_0))) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_5_1__altcat_1,e1_5_1__altcat_1])],[e5_5_1__altcat_1,i3_5_1__altcat_1]),
    [interesting(0.65),file(altcat_1,i2_5_1__altcat_1),[file(altcat_1,i2_5_1__altcat_1)]]).

fof(i1_5_1__altcat_1,plain,
    ( r2_hidden(c1_5_1__altcat_1,k1_funct_2(k1_xboole_0,k1_xboole_0))
   => r2_hidden(c1_5_1__altcat_1,k1_tarski(k6_relat_1(k1_xboole_0))) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_5_1__altcat_1]),discharge_asm(discharge,[e1_5_1__altcat_1])],[e1_5_1__altcat_1,i2_5_1__altcat_1]),
    [interesting(0.65),file(altcat_1,i1_5_1__altcat_1),[file(altcat_1,i1_5_1__altcat_1)]]).

fof(i1_5_1_tmp__altcat_1,plain,
    ( r2_hidden(c1_5_1__altcat_1,k1_funct_2(k1_xboole_0,k1_xboole_0))
   => r2_hidden(c1_5_1__altcat_1,k1_tarski(k6_relat_1(k1_xboole_0))) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_5_1__altcat_1])],[dt_c1_5_1__altcat_1,i1_5_1__altcat_1]),
    [interesting(0.8),e1_5__altcat_1]).

fof(e1_5__altcat_1,plain,(
    ! [A] : 
      ( r2_hidden(A,k1_funct_2(k1_xboole_0,k1_xboole_0))
     => r2_hidden(A,k1_tarski(k6_relat_1(k1_xboole_0))) ) ),
    inference(let,[status(thm),assumptions([])],[i1_5_1_tmp__altcat_1,dh_c1_5_1__altcat_1]),
    [interesting(0.8),file(altcat_1,e1_5__altcat_1),[file(altcat_1,e1_5__altcat_1)]]).

fof(t2_altcat_1,theorem,(
    ! [A] : r2_hidden(k6_relat_1(A),k1_funct_2(A,A)) ),
    file(altcat_1,t2_altcat_1),
    [interesting(0.9),axiom,file(altcat_1,t2_altcat_1)]).

fof(e2_5__altcat_1,plain,(
    r2_hidden(k6_relat_1(k1_xboole_0),k1_funct_2(k1_xboole_0,k1_xboole_0)) ),
    inference(mizar_by,[status(thm),assumptions([])],[rc3_funct_1,existence_m1_subset_1,dt_m1_subset_1,cc1_fraenkel,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc1_funct_2,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_k6_relat_1,fc12_relat_1,fc1_fraenkel,fc2_funct_1,fc2_funct_2,fc4_relat_1,t1_subset,t6_boole,t7_boole,t2_altcat_1]),
    [interesting(0.8),file(altcat_1,e2_5__altcat_1),[file(altcat_1,e2_5__altcat_1)]]).

fof(t37_zfmisc_1,theorem,(
    ! [A,B] : 
      ( r1_tarski(k1_tarski(A),B)
    <=> r2_hidden(A,B) ) ),
    file(zfmisc_1,t37_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,t37_zfmisc_1)]).

fof(e3_5__altcat_1,plain,(
    r1_tarski(k1_tarski(k6_relat_1(k1_xboole_0)),k1_funct_2(k1_xboole_0,k1_xboole_0)) ),
    inference(mizar_by,[status(thm),assumptions([])],[cc1_tex_2,cc3_tex_2,cc5_tex_2,cc7_tex_2,rc2_tex_2,rc3_funct_1,rc3_tex_2,rc4_tex_2,rc6_tex_2,rc7_tex_2,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,cc1_altcat_1,cc1_fraenkel,cc1_funct_1,cc1_relat_1,cc2_funct_1,cc2_tex_2,cc4_tex_2,cc6_tex_2,fc1_funct_2,fc1_subset_1,fc2_altcat_1,fc2_fraenkel,rc1_fraenkel,rc1_funct_1,rc1_relat_1,rc1_subset_1,rc1_tex_2,rc2_funct_1,rc2_relat_1,rc2_subset_1,rc3_relat_1,rc4_funct_1,rc5_tex_2,t2_subset,t4_subset,t5_subset,t8_boole,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_funct_2,dt_k1_tarski,dt_k1_xboole_0,dt_k6_relat_1,fc12_relat_1,fc1_fraenkel,fc1_tex_2,fc2_funct_1,fc2_funct_2,fc2_subset_1,fc4_relat_1,t1_subset,t3_subset,t6_boole,t7_boole,e2_5__altcat_1,t37_zfmisc_1]),
    [interesting(0.8),file(altcat_1,e3_5__altcat_1),[file(altcat_1,e3_5__altcat_1)]]).

fof(i2_5__altcat_1,theorem,(
    $true ),
    introduced(tautology,[file(altcat_1,i2_5__altcat_1)]),
    [interesting(0.8),trivial,file(altcat_1,i2_5__altcat_1)]).

fof(i1_5__altcat_1,plain,(
    r1_tarski(k1_tarski(k6_relat_1(k1_xboole_0)),k1_funct_2(k1_xboole_0,k1_xboole_0)) ),
    inference(conclusion,[status(thm),assumptions([])],[e3_5__altcat_1,i2_5__altcat_1]),
    [interesting(0.8),file(altcat_1,i1_5__altcat_1),[file(altcat_1,i1_5__altcat_1)]]).

fof(t3_altcat_1,theorem,(
    k1_funct_2(k1_xboole_0,k1_xboole_0) = k1_tarski(k6_relat_1(k1_xboole_0)) ),
    inference(conclusion,[status(thm),assumptions([])],[rc3_funct_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc1_funct_2,fc2_altcat_1,fc2_fraenkel,rc1_fraenkel,rc1_funct_1,rc1_relat_1,rc1_tex_2,rc2_funct_1,rc2_relat_1,rc3_relat_1,rc4_funct_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_funct_2,dt_k1_tarski,dt_k1_xboole_0,dt_k6_relat_1,fc12_relat_1,fc1_fraenkel,fc1_tex_2,fc2_funct_1,fc2_funct_2,fc2_subset_1,fc4_relat_1,d3_tarski,d10_xboole_0,e1_5__altcat_1,i1_5__altcat_1]),
    [interesting(1),file(altcat_1,t3_altcat_1),[file(altcat_1,t3_altcat_1)]]).