% Mizar ND problem: t7_autalg_1,autalg_1,189,56 
fof(dh_c1_8__autalg_1,definition,
    ( ( ( ~ v3_struct_0(c1_8__autalg_1)
        & v6_unialg_1(c1_8__autalg_1)
        & v7_unialg_1(c1_8__autalg_1)
        & v8_unialg_1(c1_8__autalg_1)
        & l1_unialg_1(c1_8__autalg_1) )
     => ! [A] : 
          ( m2_fraenkel(A,u1_struct_0(c1_8__autalg_1),u1_struct_0(c1_8__autalg_1),k1_autalg_1(c1_8__autalg_1))
         => ! [B] : 
              ( m2_fraenkel(B,u1_struct_0(c1_8__autalg_1),u1_struct_0(c1_8__autalg_1),k1_autalg_1(c1_8__autalg_1))
             => r2_hidden(k7_funct_2(u1_struct_0(c1_8__autalg_1),u1_struct_0(c1_8__autalg_1),u1_struct_0(c1_8__autalg_1),B,A),k1_autalg_1(c1_8__autalg_1)) ) ) )
   => ! [C] : 
        ( ( ~ v3_struct_0(C)
          & v6_unialg_1(C)
          & v7_unialg_1(C)
          & v8_unialg_1(C)
          & l1_unialg_1(C) )
       => ! [D] : 
            ( m2_fraenkel(D,u1_struct_0(C),u1_struct_0(C),k1_autalg_1(C))
           => ! [E] : 
                ( m2_fraenkel(E,u1_struct_0(C),u1_struct_0(C),k1_autalg_1(C))
               => r2_hidden(k7_funct_2(u1_struct_0(C),u1_struct_0(C),u1_struct_0(C),E,D),k1_autalg_1(C)) ) ) ) ),
    introduced(definition,[new_symbol(c1_8__autalg_1),file(autalg_1,c1_8__autalg_1)]),
    [interesting(0.8),axiom,file(autalg_1,c1_8__autalg_1)]).

fof(dh_c2_8__autalg_1,definition,
    ( ( m2_fraenkel(c2_8__autalg_1,u1_struct_0(c1_8__autalg_1),u1_struct_0(c1_8__autalg_1),k1_autalg_1(c1_8__autalg_1))
     => ! [A] : 
          ( m2_fraenkel(A,u1_struct_0(c1_8__autalg_1),u1_struct_0(c1_8__autalg_1),k1_autalg_1(c1_8__autalg_1))
         => r2_hidden(k7_funct_2(u1_struct_0(c1_8__autalg_1),u1_struct_0(c1_8__autalg_1),u1_struct_0(c1_8__autalg_1),A,c2_8__autalg_1),k1_autalg_1(c1_8__autalg_1)) ) )
   => ! [B] : 
        ( m2_fraenkel(B,u1_struct_0(c1_8__autalg_1),u1_struct_0(c1_8__autalg_1),k1_autalg_1(c1_8__autalg_1))
       => ! [C] : 
            ( m2_fraenkel(C,u1_struct_0(c1_8__autalg_1),u1_struct_0(c1_8__autalg_1),k1_autalg_1(c1_8__autalg_1))
           => r2_hidden(k7_funct_2(u1_struct_0(c1_8__autalg_1),u1_struct_0(c1_8__autalg_1),u1_struct_0(c1_8__autalg_1),C,B),k1_autalg_1(c1_8__autalg_1)) ) ) ),
    introduced(definition,[new_symbol(c2_8__autalg_1),file(autalg_1,c2_8__autalg_1)]),
    [interesting(0.8),axiom,file(autalg_1,c2_8__autalg_1)]).

fof(dh_c3_8__autalg_1,definition,
    ( ( m2_fraenkel(c3_8__autalg_1,u1_struct_0(c1_8__autalg_1),u1_struct_0(c1_8__autalg_1),k1_autalg_1(c1_8__autalg_1))
     => r2_hidden(k7_funct_2(u1_struct_0(c1_8__autalg_1),u1_struct_0(c1_8__autalg_1),u1_struct_0(c1_8__autalg_1),c3_8__autalg_1,c2_8__autalg_1),k1_autalg_1(c1_8__autalg_1)) )
   => ! [A] : 
        ( m2_fraenkel(A,u1_struct_0(c1_8__autalg_1),u1_struct_0(c1_8__autalg_1),k1_autalg_1(c1_8__autalg_1))
       => r2_hidden(k7_funct_2(u1_struct_0(c1_8__autalg_1),u1_struct_0(c1_8__autalg_1),u1_struct_0(c1_8__autalg_1),A,c2_8__autalg_1),k1_autalg_1(c1_8__autalg_1)) ) ),
    introduced(definition,[new_symbol(c3_8__autalg_1),file(autalg_1,c3_8__autalg_1)]),
    [interesting(0.8),axiom,file(autalg_1,c3_8__autalg_1)]).

fof(rc1_partfun1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_xboole_0(A) ) ),
    file(partfun1,rc1_partfun1),
    [interesting(0.9),axiom,file(partfun1,rc1_partfun1)]).

fof(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(reflexivity_r1_tarski,theorem,(
    ! [A,B] : r1_tarski(A,A) ),
    file(tarski,r1_tarski),
    [interesting(0.9),axiom,file(tarski,r1_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(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(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_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(fc1_xboole_0,theorem,(
    v1_xboole_0(k1_xboole_0) ),
    file(xboole_0,fc1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,fc1_xboole_0)]).

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_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(rc2_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_xboole_0(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc2_funct_1),
    [interesting(0.9),axiom,file(funct_1,rc2_funct_1)]).

fof(rc2_partfun1,theorem,(
    ! [A,B] : 
    ? [C] : 
      ( m1_relset_1(C,A,B)
      & v1_relat_1(C)
      & v1_funct_1(C) ) ),
    file(partfun1,rc2_partfun1),
    [interesting(0.9),axiom,file(partfun1,rc2_partfun1)]).

fof(existence_l1_struct_0,axiom,(
    ? [A] : l1_struct_0(A) ),
    file(struct_0,l1_struct_0),
    [interesting(0.9),axiom,file(struct_0,l1_struct_0)]).

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

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

fof(dt_k1_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k1_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,k1_zfmisc_1)]).

fof(dt_k2_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k2_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,k2_zfmisc_1)]).

fof(dt_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(dt_l1_struct_0,axiom,(
    $true ),
    file(struct_0,l1_struct_0),
    [interesting(0.9),axiom,file(struct_0,l1_struct_0)]).

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_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_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(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_struct_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ~ v1_xboole_0(u1_struct_0(A)) ) ),
    file(struct_0,fc1_struct_0),
    [interesting(0.9),axiom,file(struct_0,fc1_struct_0)]).

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

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(rc1_xboole_0,theorem,(
    ? [A] : v1_xboole_0(A) ),
    file(xboole_0,rc1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,rc1_xboole_0)]).

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(rc2_xboole_0,theorem,(
    ? [A] : ~ v1_xboole_0(A) ),
    file(xboole_0,rc2_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,rc2_xboole_0)]).

fof(rc3_struct_0,theorem,(
    ? [A] : 
      ( l1_struct_0(A)
      & ~ v3_struct_0(A) ) ),
    file(struct_0,rc3_struct_0),
    [interesting(0.9),axiom,file(struct_0,rc3_struct_0)]).

fof(rc5_struct_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & ~ v1_xboole_0(B) ) ) ),
    file(struct_0,rc5_struct_0),
    [interesting(0.9),axiom,file(struct_0,rc5_struct_0)]).

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

fof(t3_subset,theorem,(
    ! [A,B] : 
      ( m1_subset_1(A,k1_zfmisc_1(B))
    <=> r1_tarski(A,B) ) ),
    file(subset,t3_subset),
    [interesting(0.9),axiom,file(subset,t3_subset)]).

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

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

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

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

fof(existence_l1_unialg_1,axiom,(
    ? [A] : l1_unialg_1(A) ),
    file(unialg_1,l1_unialg_1),
    [interesting(0.9),axiom,file(unialg_1,l1_unialg_1)]).

fof(existence_m1_fraenkel,axiom,(
    ! [A,B] : 
    ? [C] : m1_fraenkel(C,A,B) ),
    file(fraenkel,m1_fraenkel),
    [interesting(0.9),axiom,file(fraenkel,m1_fraenkel)]).

fof(existence_m2_fraenkel,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(B)
        & m1_fraenkel(C,A,B) )
     => ? [D] : m2_fraenkel(D,A,B,C) ) ),
    file(fraenkel,m2_fraenkel),
    [interesting(0.9),axiom,file(fraenkel,m2_fraenkel)]).

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_k7_funct_2,definition,(
    ! [A,B,C,D,E] : 
      ( ( ~ v1_xboole_0(B)
        & v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m1_relset_1(D,A,B)
        & v1_funct_1(E)
        & v1_funct_2(E,B,C)
        & m1_relset_1(E,B,C) )
     => k7_funct_2(A,B,C,D,E) = k5_relat_1(D,E) ) ),
    file(funct_2,k7_funct_2),
    [interesting(0.9),axiom,file(funct_2,k7_funct_2)]).

fof(redefinition_m2_fraenkel,definition,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(B)
        & m1_fraenkel(C,A,B) )
     => ! [D] : 
          ( m2_fraenkel(D,A,B,C)
        <=> m1_subset_1(D,C) ) ) ),
    file(fraenkel,m2_fraenkel),
    [interesting(0.9),axiom,file(fraenkel,m2_fraenkel)]).

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_autalg_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => m1_fraenkel(k1_autalg_1(A),u1_struct_0(A),u1_struct_0(A)) ) ),
    file(autalg_1,k1_autalg_1),
    [interesting(0.9),axiom,file(autalg_1,k1_autalg_1)]).

fof(dt_k7_funct_2,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v1_xboole_0(B)
        & v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m1_relset_1(D,A,B)
        & v1_funct_1(E)
        & v1_funct_2(E,B,C)
        & m1_relset_1(E,B,C) )
     => ( v1_funct_1(k7_funct_2(A,B,C,D,E))
        & v1_funct_2(k7_funct_2(A,B,C,D,E),A,C)
        & m2_relset_1(k7_funct_2(A,B,C,D,E),A,C) ) ) ),
    file(funct_2,k7_funct_2),
    [interesting(0.9),axiom,file(funct_2,k7_funct_2)]).

fof(dt_l1_unialg_1,axiom,(
    ! [A] : 
      ( l1_unialg_1(A)
     => l1_struct_0(A) ) ),
    file(unialg_1,l1_unialg_1),
    [interesting(0.9),axiom,file(unialg_1,l1_unialg_1)]).

fof(dt_m1_fraenkel,axiom,(
    ! [A,B,C] : 
      ( m1_fraenkel(C,A,B)
     => ( ~ v1_xboole_0(C)
        & v1_fraenkel(C) ) ) ),
    file(fraenkel,m1_fraenkel),
    [interesting(0.9),axiom,file(fraenkel,m1_fraenkel)]).

fof(dt_m2_fraenkel,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(B)
        & m1_fraenkel(C,A,B) )
     => ! [D] : 
          ( m2_fraenkel(D,A,B,C)
         => ( v1_funct_1(D)
            & v1_funct_2(D,A,B)
            & m2_relset_1(D,A,B) ) ) ) ),
    file(fraenkel,m2_fraenkel),
    [interesting(0.9),axiom,file(fraenkel,m2_fraenkel)]).

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_u1_struct_0,axiom,(
    $true ),
    file(struct_0,u1_struct_0),
    [interesting(0.9),axiom,file(struct_0,u1_struct_0)]).

fof(dt_c1_8__autalg_1,assumption,
    ( ~ v3_struct_0(c1_8__autalg_1)
    & v6_unialg_1(c1_8__autalg_1)
    & v7_unialg_1(c1_8__autalg_1)
    & v8_unialg_1(c1_8__autalg_1)
    & l1_unialg_1(c1_8__autalg_1) ),
    introduced(assumption,[file(autalg_1,c1_8__autalg_1)]),
    [interesting(0.8),axiom,file(autalg_1,c1_8__autalg_1)]).

fof(dt_c2_8__autalg_1,assumption,(
    m2_fraenkel(c2_8__autalg_1,u1_struct_0(c1_8__autalg_1),u1_struct_0(c1_8__autalg_1),k1_autalg_1(c1_8__autalg_1)) ),
    introduced(assumption,[file(autalg_1,c2_8__autalg_1)]),
    [interesting(0.8),axiom,file(autalg_1,c2_8__autalg_1)]).

fof(dt_c3_8__autalg_1,assumption,(
    m2_fraenkel(c3_8__autalg_1,u1_struct_0(c1_8__autalg_1),u1_struct_0(c1_8__autalg_1),k1_autalg_1(c1_8__autalg_1)) ),
    introduced(assumption,[file(autalg_1,c3_8__autalg_1)]),
    [interesting(0.8),axiom,file(autalg_1,c3_8__autalg_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(d1_autalg_1,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( m1_fraenkel(B,u1_struct_0(A),u1_struct_0(A))
         => ( B = k1_autalg_1(A)
          <=> ( ! [C] : 
                  ( m2_fraenkel(C,u1_struct_0(A),u1_struct_0(A),B)
                 => ( v1_funct_1(C)
                    & v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
                    & m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) ) )
              & ! [C] : 
                  ( ( v1_funct_1(C)
                    & v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
                    & m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
                 => ( r2_hidden(C,B)
                  <=> r4_alg_1(A,A,C) ) ) ) ) ) ) ),
    file(autalg_1,d1_autalg_1),
    [interesting(0.9),axiom,file(autalg_1,d1_autalg_1)]).

fof(e1_8__autalg_1,plain,
    ( r4_alg_1(c1_8__autalg_1,c1_8__autalg_1,c2_8__autalg_1)
    & r4_alg_1(c1_8__autalg_1,c1_8__autalg_1,c3_8__autalg_1) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_8__autalg_1,dt_c2_8__autalg_1,dt_c3_8__autalg_1])],[rc1_partfun1,rc3_funct_1,reflexivity_r1_tarski,dt_k1_xboole_0,cc1_funct_2,cc2_funct_1,fc1_xboole_0,rc1_funct_1,rc1_funct_2,rc2_funct_1,rc2_partfun1,existence_l1_struct_0,existence_m1_relset_1,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_l1_struct_0,dt_m1_relset_1,dt_m1_subset_1,cc1_fraenkel,cc1_funct_1,cc1_relset_1,cc5_funct_2,cc6_funct_2,fc1_struct_0,fc1_subset_1,fc4_subset_1,rc1_fraenkel,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,rc3_struct_0,rc5_struct_0,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,existence_l1_unialg_1,existence_m1_fraenkel,existence_m2_fraenkel,existence_m2_relset_1,redefinition_m2_fraenkel,redefinition_m2_relset_1,dt_k1_autalg_1,dt_l1_unialg_1,dt_m1_fraenkel,dt_m2_fraenkel,dt_m2_relset_1,dt_u1_struct_0,dt_c1_8__autalg_1,dt_c2_8__autalg_1,dt_c3_8__autalg_1,t1_subset,t7_boole,d1_autalg_1]),
    [interesting(0.8),file(autalg_1,e1_8__autalg_1),[file(autalg_1,e1_8__autalg_1)]]).

fof(t12_alg_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v6_unialg_1(B)
            & v7_unialg_1(B)
            & v8_unialg_1(B)
            & l1_unialg_1(B) )
         => ! [C] : 
              ( ( ~ v3_struct_0(C)
                & v6_unialg_1(C)
                & v7_unialg_1(C)
                & v8_unialg_1(C)
                & l1_unialg_1(C) )
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
                    & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
                 => ! [E] : 
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(B),u1_struct_0(C))
                        & m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) )
                     => ( ( r4_alg_1(A,B,D)
                          & r4_alg_1(B,C,E) )
                       => r4_alg_1(A,C,k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E)) ) ) ) ) ) ) ),
    file(alg_1,t12_alg_1),
    [interesting(0.9),axiom,file(alg_1,t12_alg_1)]).

fof(e2_8__autalg_1,plain,(
    r4_alg_1(c1_8__autalg_1,c1_8__autalg_1,k7_funct_2(u1_struct_0(c1_8__autalg_1),u1_struct_0(c1_8__autalg_1),u1_struct_0(c1_8__autalg_1),c3_8__autalg_1,c2_8__autalg_1)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_8__autalg_1,dt_c2_8__autalg_1,dt_c3_8__autalg_1])],[cc1_fraenkel,rc1_fraenkel,rc1_partfun1,rc3_funct_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_m1_fraenkel,dt_k1_xboole_0,dt_m1_fraenkel,cc1_funct_2,cc2_funct_1,fc1_funct_1,fc1_xboole_0,rc1_funct_1,rc1_funct_2,rc2_funct_1,rc2_partfun1,t1_subset,t4_subset,t5_subset,existence_l1_struct_0,existence_m1_relset_1,existence_m1_subset_1,existence_m2_fraenkel,redefinition_m2_fraenkel,dt_k1_autalg_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k5_relat_1,dt_l1_struct_0,dt_m1_relset_1,dt_m1_subset_1,dt_m2_fraenkel,cc1_funct_1,cc1_relset_1,cc5_funct_2,cc6_funct_2,fc1_struct_0,fc1_subset_1,fc4_subset_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,rc3_struct_0,rc5_struct_0,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,existence_l1_unialg_1,existence_m2_relset_1,redefinition_k7_funct_2,redefinition_m2_relset_1,dt_k7_funct_2,dt_l1_unialg_1,dt_m2_relset_1,dt_u1_struct_0,dt_c1_8__autalg_1,dt_c2_8__autalg_1,dt_c3_8__autalg_1,e1_8__autalg_1,t12_alg_1]),
    [interesting(0.8),file(autalg_1,e2_8__autalg_1),[file(autalg_1,e2_8__autalg_1)]]).

fof(e3_8__autalg_1,plain,(
    r2_hidden(k7_funct_2(u1_struct_0(c1_8__autalg_1),u1_struct_0(c1_8__autalg_1),u1_struct_0(c1_8__autalg_1),c3_8__autalg_1,c2_8__autalg_1),k1_autalg_1(c1_8__autalg_1)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_8__autalg_1,dt_c2_8__autalg_1,dt_c3_8__autalg_1])],[rc1_partfun1,rc3_funct_1,reflexivity_r1_tarski,dt_k1_xboole_0,cc1_funct_2,cc2_funct_1,fc1_funct_1,fc1_xboole_0,rc1_funct_1,rc1_funct_2,rc2_funct_1,rc2_partfun1,existence_l1_struct_0,existence_m1_relset_1,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k5_relat_1,dt_l1_struct_0,dt_m1_relset_1,dt_m1_subset_1,cc1_fraenkel,cc1_funct_1,cc1_relset_1,cc5_funct_2,cc6_funct_2,fc1_struct_0,fc1_subset_1,fc4_subset_1,rc1_fraenkel,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,rc3_struct_0,rc5_struct_0,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,existence_l1_unialg_1,existence_m1_fraenkel,existence_m2_fraenkel,existence_m2_relset_1,redefinition_k7_funct_2,redefinition_m2_fraenkel,redefinition_m2_relset_1,dt_k1_autalg_1,dt_k7_funct_2,dt_l1_unialg_1,dt_m1_fraenkel,dt_m2_fraenkel,dt_m2_relset_1,dt_u1_struct_0,dt_c1_8__autalg_1,dt_c2_8__autalg_1,dt_c3_8__autalg_1,t1_subset,t7_boole,e2_8__autalg_1,d1_autalg_1]),
    [interesting(0.8),file(autalg_1,e3_8__autalg_1),[file(autalg_1,e3_8__autalg_1)]]).

fof(i3_8__autalg_1,theorem,(
    $true ),
    introduced(tautology,[file(autalg_1,i3_8__autalg_1)]),
    [interesting(0.8),trivial,file(autalg_1,i3_8__autalg_1)]).

fof(i2_8__autalg_1,plain,(
    r2_hidden(k7_funct_2(u1_struct_0(c1_8__autalg_1),u1_struct_0(c1_8__autalg_1),u1_struct_0(c1_8__autalg_1),c3_8__autalg_1,c2_8__autalg_1),k1_autalg_1(c1_8__autalg_1)) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_8__autalg_1,dt_c2_8__autalg_1,dt_c3_8__autalg_1])],[e3_8__autalg_1,i3_8__autalg_1]),
    [interesting(0.8),file(autalg_1,i2_8__autalg_1),[file(autalg_1,i2_8__autalg_1)]]).

fof(i2_8_tmp__autalg_1,plain,
    ( ( m2_fraenkel(c2_8__autalg_1,u1_struct_0(c1_8__autalg_1),u1_struct_0(c1_8__autalg_1),k1_autalg_1(c1_8__autalg_1))
      & m2_fraenkel(c3_8__autalg_1,u1_struct_0(c1_8__autalg_1),u1_struct_0(c1_8__autalg_1),k1_autalg_1(c1_8__autalg_1)) )
   => r2_hidden(k7_funct_2(u1_struct_0(c1_8__autalg_1),u1_struct_0(c1_8__autalg_1),u1_struct_0(c1_8__autalg_1),c3_8__autalg_1,c2_8__autalg_1),k1_autalg_1(c1_8__autalg_1)) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_8__autalg_1]),discharge_asm(discharge,[dt_c2_8__autalg_1,dt_c3_8__autalg_1])],[dt_c2_8__autalg_1,dt_c3_8__autalg_1,i2_8__autalg_1]),
    [interesting(0.8),i1_8__autalg_1]).

fof(i1_8__autalg_1,plain,(
    ! [A] : 
      ( m2_fraenkel(A,u1_struct_0(c1_8__autalg_1),u1_struct_0(c1_8__autalg_1),k1_autalg_1(c1_8__autalg_1))
     => ! [B] : 
          ( m2_fraenkel(B,u1_struct_0(c1_8__autalg_1),u1_struct_0(c1_8__autalg_1),k1_autalg_1(c1_8__autalg_1))
         => r2_hidden(k7_funct_2(u1_struct_0(c1_8__autalg_1),u1_struct_0(c1_8__autalg_1),u1_struct_0(c1_8__autalg_1),B,A),k1_autalg_1(c1_8__autalg_1)) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_8__autalg_1])],[i2_8_tmp__autalg_1,dh_c2_8__autalg_1,dh_c3_8__autalg_1]),
    [interesting(0.8),file(autalg_1,i1_8__autalg_1),[file(autalg_1,i1_8__autalg_1)]]).

fof(i1_8_tmp__autalg_1,plain,
    ( ( ~ v3_struct_0(c1_8__autalg_1)
      & v6_unialg_1(c1_8__autalg_1)
      & v7_unialg_1(c1_8__autalg_1)
      & v8_unialg_1(c1_8__autalg_1)
      & l1_unialg_1(c1_8__autalg_1) )
   => ! [A] : 
        ( m2_fraenkel(A,u1_struct_0(c1_8__autalg_1),u1_struct_0(c1_8__autalg_1),k1_autalg_1(c1_8__autalg_1))
       => ! [B] : 
            ( m2_fraenkel(B,u1_struct_0(c1_8__autalg_1),u1_struct_0(c1_8__autalg_1),k1_autalg_1(c1_8__autalg_1))
           => r2_hidden(k7_funct_2(u1_struct_0(c1_8__autalg_1),u1_struct_0(c1_8__autalg_1),u1_struct_0(c1_8__autalg_1),B,A),k1_autalg_1(c1_8__autalg_1)) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_8__autalg_1])],[dt_c1_8__autalg_1,i1_8__autalg_1]),
    [interesting(1),t7_autalg_1]).

fof(t7_autalg_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( m2_fraenkel(B,u1_struct_0(A),u1_struct_0(A),k1_autalg_1(A))
         => ! [C] : 
              ( m2_fraenkel(C,u1_struct_0(A),u1_struct_0(A),k1_autalg_1(A))
             => r2_hidden(k7_funct_2(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),C,B),k1_autalg_1(A)) ) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_8_tmp__autalg_1,dh_c1_8__autalg_1]),
    [interesting(1),file(autalg_1,t7_autalg_1),[file(autalg_1,t7_autalg_1)]]).