% Mizar ND problem: t1_armstrng,armstrng,45,35 
fof(dh_c1_2__armstrng,definition,
    ( ( v2_finsub_1(c1_2__armstrng)
     => ! [A,B] : 
          ( ( v1_finset_1(B)
            & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
         => ( ( r2_hidden(A,c1_2__armstrng)
              & r1_tarski(B,c1_2__armstrng) )
           => r2_hidden(k8_setfam_1(A,B),c1_2__armstrng) ) ) )
   => ! [C] : 
        ( v2_finsub_1(C)
       => ! [D,E] : 
            ( ( v1_finset_1(E)
              & m1_subset_1(E,k1_zfmisc_1(k1_zfmisc_1(D))) )
           => ( ( r2_hidden(D,C)
                & r1_tarski(E,C) )
             => r2_hidden(k8_setfam_1(D,E),C) ) ) ) ),
    introduced(definition,[new_symbol(c1_2__armstrng),file(armstrng,c1_2__armstrng)]),
    [interesting(0.8),axiom,file(armstrng,c1_2__armstrng)]).

fof(e1_2__armstrng,assumption,(
    v2_finsub_1(c1_2__armstrng) ),
    introduced(assumption,[file(armstrng,e1_2__armstrng)]),
    [interesting(0.8),axiom,file(armstrng,e1_2__armstrng)]).

fof(dh_c2_2__armstrng,definition,
    ( ! [A] : 
        ( ( v1_finset_1(A)
          & m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(c2_2__armstrng))) )
       => ( ( r2_hidden(c2_2__armstrng,c1_2__armstrng)
            & r1_tarski(A,c1_2__armstrng) )
         => r2_hidden(k8_setfam_1(c2_2__armstrng,A),c1_2__armstrng) ) )
   => ! [B,C] : 
        ( ( v1_finset_1(C)
          & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(B))) )
       => ( ( r2_hidden(B,c1_2__armstrng)
            & r1_tarski(C,c1_2__armstrng) )
         => r2_hidden(k8_setfam_1(B,C),c1_2__armstrng) ) ) ),
    introduced(definition,[new_symbol(c2_2__armstrng),file(armstrng,c2_2__armstrng)]),
    [interesting(0.8),axiom,file(armstrng,c2_2__armstrng)]).

fof(dh_c3_2__armstrng,definition,
    ( ( ( v1_finset_1(c3_2__armstrng)
        & m1_subset_1(c3_2__armstrng,k1_zfmisc_1(k1_zfmisc_1(c2_2__armstrng))) )
     => ( ( r2_hidden(c2_2__armstrng,c1_2__armstrng)
          & r1_tarski(c3_2__armstrng,c1_2__armstrng) )
       => r2_hidden(k8_setfam_1(c2_2__armstrng,c3_2__armstrng),c1_2__armstrng) ) )
   => ! [A] : 
        ( ( v1_finset_1(A)
          & m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(c2_2__armstrng))) )
       => ( ( r2_hidden(c2_2__armstrng,c1_2__armstrng)
            & r1_tarski(A,c1_2__armstrng) )
         => r2_hidden(k8_setfam_1(c2_2__armstrng,A),c1_2__armstrng) ) ) ),
    introduced(definition,[new_symbol(c3_2__armstrng),file(armstrng,c3_2__armstrng)]),
    [interesting(0.8),axiom,file(armstrng,c3_2__armstrng)]).

fof(e2_2__armstrng,assumption,(
    r2_hidden(c2_2__armstrng,c1_2__armstrng) ),
    introduced(assumption,[file(armstrng,e2_2__armstrng)]),
    [interesting(0.8),axiom,file(armstrng,e2_2__armstrng)]).

fof(e3_2__armstrng,assumption,(
    r1_tarski(c3_2__armstrng,c1_2__armstrng) ),
    introduced(assumption,[file(armstrng,e3_2__armstrng)]),
    [interesting(0.8),axiom,file(armstrng,e3_2__armstrng)]).

fof(cc1_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finset_1(A) ) ) ),
    file(finseq_1,cc1_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,cc1_finseq_1)]).

fof(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_finseq_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finseq_1(A) ) ),
    file(finseq_1,rc1_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,rc1_finseq_1)]).

fof(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_margrel1,theorem,(
    ? [A] : v1_margrel1(A) ),
    file(margrel1,rc1_margrel1),
    [interesting(0.9),axiom,file(margrel1,rc1_margrel1)]).

fof(rc1_pboole,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v3_relat_1(A)
      & v1_funct_1(A) ) ),
    file(pboole,rc1_pboole),
    [interesting(0.9),axiom,file(pboole,rc1_pboole)]).

fof(rc2_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(rc3_finseq_1,theorem,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_finset_1(A)
      & v1_finseq_1(A) ) ),
    file(finseq_1,rc3_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,rc3_finseq_1)]).

fof(rc3_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(rc4_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v3_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc4_funct_1),
    [interesting(0.9),axiom,file(funct_1,rc4_funct_1)]).

fof(rc6_finseq_1,theorem,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_finset_1(A) ) ),
    file(finseq_1,rc6_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,rc6_finseq_1)]).

fof(rc7_finseq_1,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A) ) ),
    file(finseq_1,rc7_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,rc7_finseq_1)]).

fof(rc8_finseq_1,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A)
      & v1_finseq_1(A) ) ),
    file(finseq_1,rc8_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,rc8_finseq_1)]).

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

fof(fc1_margrel1,theorem,
    ( v1_xboole_0(k1_xboole_0)
    & v1_margrel1(k1_xboole_0) ),
    file(margrel1,fc1_margrel1),
    [interesting(0.9),axiom,file(margrel1,fc1_margrel1)]).

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(fc2_finseq_1,theorem,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0)
    & v3_relat_1(k1_xboole_0)
    & v1_funct_1(k1_xboole_0)
    & v2_funct_1(k1_xboole_0)
    & v1_finset_1(k1_xboole_0)
    & v1_finseq_1(k1_xboole_0) ),
    file(finseq_1,fc2_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,fc2_finseq_1)]).

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

fof(cc1_finset_1,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_finset_1(A) ) ),
    file(finset_1,cc1_finset_1),
    [interesting(0.9),axiom,file(finset_1,cc1_finset_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(cc2_finset_1,theorem,(
    ! [A] : 
      ( v1_finset_1(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => v1_finset_1(B) ) ) ),
    file(finset_1,cc2_finset_1),
    [interesting(0.9),axiom,file(finset_1,cc2_finset_1)]).

fof(rc1_finset_1,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_finset_1(A) ) ),
    file(finset_1,rc1_finset_1),
    [interesting(0.9),axiom,file(finset_1,rc1_finset_1)]).

fof(rc1_subset_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B) ) ) ),
    file(subset_1,rc1_subset_1),
    [interesting(0.9),axiom,file(subset_1,rc1_subset_1)]).

fof(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_finset_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & v1_finset_1(B) ) ) ),
    file(finset_1,rc3_finset_1),
    [interesting(0.9),axiom,file(finset_1,rc3_finset_1)]).

fof(rc4_finset_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & v1_finset_1(B) ) ) ),
    file(finset_1,rc4_finset_1),
    [interesting(0.9),axiom,file(finset_1,rc4_finset_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(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_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_k8_setfam_1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => m1_subset_1(k8_setfam_1(A,B),k1_zfmisc_1(A)) ) ),
    file(setfam_1,k8_setfam_1),
    [interesting(0.9),axiom,file(setfam_1,k8_setfam_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_c1_2__armstrng,assumption,(
    $true ),
    introduced(assumption,[file(armstrng,c1_2__armstrng)]),
    [interesting(0.8),axiom,file(armstrng,c1_2__armstrng)]).

fof(dt_c2_2__armstrng,assumption,(
    $true ),
    introduced(assumption,[file(armstrng,c2_2__armstrng)]),
    [interesting(0.8),axiom,file(armstrng,c2_2__armstrng)]).

fof(dt_c3_2__armstrng,assumption,
    ( v1_finset_1(c3_2__armstrng)
    & m1_subset_1(c3_2__armstrng,k1_zfmisc_1(k1_zfmisc_1(c2_2__armstrng))) ),
    introduced(assumption,[file(armstrng,c3_2__armstrng)]),
    [interesting(0.8),axiom,file(armstrng,c3_2__armstrng)]).

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

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

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

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

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_xboole_0,theorem,(
    ! [A,B] : 
      ( ~ v1_xboole_0(A)
     => ~ v1_xboole_0(k2_xboole_0(A,B)) ) ),
    file(xboole_0,fc2_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,fc2_xboole_0)]).

fof(fc3_xboole_0,theorem,(
    ! [A,B] : 
      ( ~ v1_xboole_0(A)
     => ~ v1_xboole_0(k2_xboole_0(B,A)) ) ),
    file(xboole_0,fc3_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,fc3_xboole_0)]).

fof(commutativity_k2_xboole_0,theorem,(
    ! [A,B] : k2_xboole_0(A,B) = k2_xboole_0(B,A) ),
    file(xboole_0,k2_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k2_xboole_0)]).

fof(idempotence_k2_xboole_0,theorem,(
    ! [A,B] : k2_xboole_0(A,A) = A ),
    file(xboole_0,k2_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k2_xboole_0)]).

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

fof(dt_k2_xboole_0,axiom,(
    $true ),
    file(xboole_0,k2_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k2_xboole_0)]).

fof(fc1_finset_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(k1_tarski(A))
      & v1_finset_1(k1_tarski(A)) ) ),
    file(finset_1,fc1_finset_1),
    [interesting(0.9),axiom,file(finset_1,fc1_finset_1)]).

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(fc9_finset_1,theorem,(
    ! [A,B] : 
      ( ( v1_finset_1(A)
        & v1_finset_1(B) )
     => v1_finset_1(k2_xboole_0(A,B)) ) ),
    file(finset_1,fc9_finset_1),
    [interesting(0.9),axiom,file(finset_1,fc9_finset_1)]).

fof(s2_finset_1__e7_2__armstrng,theorem,(
    ! [A,B,C] : 
      ( ( v1_finset_1(C)
        & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(B))) )
     => ( ( v1_finset_1(C)
          & ! [D] : 
              ( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(B)))
             => ( D = k1_xboole_0
               => r2_hidden(k8_setfam_1(B,D),A) ) )
          & ! [E,F] : 
              ( ( r2_hidden(E,C)
                & r1_tarski(F,C)
                & ! [G] : 
                    ( m1_subset_1(G,k1_zfmisc_1(k1_zfmisc_1(B)))
                   => ( G = F
                     => r2_hidden(k8_setfam_1(B,G),A) ) ) )
             => ! [H] : 
                  ( m1_subset_1(H,k1_zfmisc_1(k1_zfmisc_1(B)))
                 => ( H = k2_xboole_0(F,k1_tarski(E))
                   => r2_hidden(k8_setfam_1(B,H),A) ) ) ) )
       => ! [I] : 
            ( m1_subset_1(I,k1_zfmisc_1(k1_zfmisc_1(B)))
           => ( I = C
             => r2_hidden(k8_setfam_1(B,I),A) ) ) ) ) ),
    file(armstrng,s2_finset_1__e7_2__armstrng),
    [interesting(0.9),axiom,file(armstrng,s2_finset_1__e7_2__armstrng)]).

fof(e4_2__armstrng,plain,(
    v1_finset_1(c3_2__armstrng) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_2__armstrng,dt_c3_2__armstrng])],[cc1_finseq_1,cc2_funct_1,rc1_finseq_1,rc1_funct_1,rc1_margrel1,rc1_pboole,rc2_funct_1,rc3_finseq_1,rc3_funct_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,antisymmetry_r2_hidden,dt_k1_xboole_0,fc1_margrel1,fc1_xboole_0,fc2_finseq_1,t1_subset,t4_subset,t5_subset,t8_boole,reflexivity_r1_tarski,cc1_finset_1,cc1_funct_1,rc1_finset_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,rc3_finset_1,rc4_finset_1,t2_subset,t6_boole,t7_boole,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,dt_c2_2__armstrng,cc2_finset_1,fc1_subset_1,t3_subset,dt_c3_2__armstrng]),
    [interesting(0.8),file(armstrng,e4_2__armstrng),[file(armstrng,e4_2__armstrng)]]).

fof(dt_k1_setfam_1,axiom,(
    $true ),
    file(setfam_1,k1_setfam_1),
    [interesting(0.9),axiom,file(setfam_1,k1_setfam_1)]).

fof(redefinition_k6_setfam_1,definition,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => k6_setfam_1(A,B) = k1_setfam_1(B) ) ),
    file(setfam_1,k6_setfam_1),
    [interesting(0.9),axiom,file(setfam_1,k6_setfam_1)]).

fof(dt_k6_setfam_1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => m1_subset_1(k6_setfam_1(A,B),k1_zfmisc_1(A)) ) ),
    file(setfam_1,k6_setfam_1),
    [interesting(0.9),axiom,file(setfam_1,k6_setfam_1)]).

fof(d10_setfam_1,definition,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ( ( B != k1_xboole_0
         => k8_setfam_1(A,B) = k6_setfam_1(A,B) )
        & ( B = k1_xboole_0
         => k8_setfam_1(A,B) = A ) ) ) ),
    file(setfam_1,d10_setfam_1),
    [interesting(0.9),axiom,file(setfam_1,d10_setfam_1)]).

fof(e5_2__armstrng,plain,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(c2_2__armstrng)))
     => ( A = k1_xboole_0
       => r2_hidden(k8_setfam_1(c2_2__armstrng,A),c1_2__armstrng) ) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2__armstrng,dt_c2_2__armstrng,e2_2__armstrng])],[reflexivity_r1_tarski,dt_k1_setfam_1,cc1_finseq_1,cc1_finset_1,cc1_funct_1,cc2_finset_1,cc2_funct_1,rc1_finseq_1,rc1_finset_1,rc1_funct_1,rc1_margrel1,rc1_pboole,rc1_subset_1,rc1_xboole_0,rc2_funct_1,rc2_subset_1,rc2_xboole_0,rc3_finseq_1,rc3_finset_1,rc3_funct_1,rc4_finset_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t5_subset,t8_boole,antisymmetry_r2_hidden,existence_m1_subset_1,redefinition_k6_setfam_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k6_setfam_1,dt_k8_setfam_1,dt_m1_subset_1,dt_c1_2__armstrng,dt_c2_2__armstrng,fc1_margrel1,fc1_subset_1,fc1_xboole_0,fc2_finseq_1,t1_subset,t3_subset,t4_subset,t6_boole,t7_boole,e2_2__armstrng,d10_setfam_1]),
    [interesting(0.8),file(armstrng,e5_2__armstrng),[file(armstrng,e5_2__armstrng)]]).

fof(dh_c1_2_1__armstrng,definition,
    ( ! [A] : 
        ( ( r2_hidden(c1_2_1__armstrng,c3_2__armstrng)
          & r1_tarski(A,c3_2__armstrng)
          & ! [B] : 
              ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(c2_2__armstrng)))
             => ( B = A
               => r2_hidden(k8_setfam_1(c2_2__armstrng,B),c1_2__armstrng) ) ) )
       => ! [B] : 
            ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(c2_2__armstrng)))
           => ( B = k2_xboole_0(A,k1_tarski(c1_2_1__armstrng))
             => r2_hidden(k8_setfam_1(c2_2__armstrng,B),c1_2__armstrng) ) ) )
   => ! [C,D] : 
        ( ( r2_hidden(C,c3_2__armstrng)
          & r1_tarski(D,c3_2__armstrng)
          & ! [E] : 
              ( m1_subset_1(E,k1_zfmisc_1(k1_zfmisc_1(c2_2__armstrng)))
             => ( E = D
               => r2_hidden(k8_setfam_1(c2_2__armstrng,E),c1_2__armstrng) ) ) )
       => ! [E] : 
            ( m1_subset_1(E,k1_zfmisc_1(k1_zfmisc_1(c2_2__armstrng)))
           => ( E = k2_xboole_0(D,k1_tarski(C))
             => r2_hidden(k8_setfam_1(c2_2__armstrng,E),c1_2__armstrng) ) ) ) ),
    introduced(definition,[new_symbol(c1_2_1__armstrng),file(armstrng,c1_2_1__armstrng)]),
    [interesting(0.65),axiom,file(armstrng,c1_2_1__armstrng)]).

fof(dh_c2_2_1__armstrng,definition,
    ( ( ( r2_hidden(c1_2_1__armstrng,c3_2__armstrng)
        & r1_tarski(c2_2_1__armstrng,c3_2__armstrng)
        & ! [A] : 
            ( m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(c2_2__armstrng)))
           => ( A = c2_2_1__armstrng
             => r2_hidden(k8_setfam_1(c2_2__armstrng,A),c1_2__armstrng) ) ) )
     => ! [A] : 
          ( m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(c2_2__armstrng)))
         => ( A = k2_xboole_0(c2_2_1__armstrng,k1_tarski(c1_2_1__armstrng))
           => r2_hidden(k8_setfam_1(c2_2__armstrng,A),c1_2__armstrng) ) ) )
   => ! [B] : 
        ( ( r2_hidden(c1_2_1__armstrng,c3_2__armstrng)
          & r1_tarski(B,c3_2__armstrng)
          & ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(c2_2__armstrng)))
             => ( C = B
               => r2_hidden(k8_setfam_1(c2_2__armstrng,C),c1_2__armstrng) ) ) )
       => ! [C] : 
            ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(c2_2__armstrng)))
           => ( C = k2_xboole_0(B,k1_tarski(c1_2_1__armstrng))
             => r2_hidden(k8_setfam_1(c2_2__armstrng,C),c1_2__armstrng) ) ) ) ),
    introduced(definition,[new_symbol(c2_2_1__armstrng),file(armstrng,c2_2_1__armstrng)]),
    [interesting(0.65),axiom,file(armstrng,c2_2_1__armstrng)]).

fof(e1_2_1__armstrng,assumption,(
    r2_hidden(c1_2_1__armstrng,c3_2__armstrng) ),
    introduced(assumption,[file(armstrng,e1_2_1__armstrng)]),
    [interesting(0.65),axiom,file(armstrng,e1_2_1__armstrng)]).

fof(e2_2_1__armstrng,assumption,(
    r1_tarski(c2_2_1__armstrng,c3_2__armstrng) ),
    introduced(assumption,[file(armstrng,e2_2_1__armstrng)]),
    [interesting(0.65),axiom,file(armstrng,e2_2_1__armstrng)]).

fof(e3_2_1__armstrng,assumption,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(c2_2__armstrng)))
     => ( A = c2_2_1__armstrng
       => r2_hidden(k8_setfam_1(c2_2__armstrng,A),c1_2__armstrng) ) ) ),
    introduced(assumption,[file(armstrng,e3_2_1__armstrng)]),
    [interesting(0.65),axiom,file(armstrng,e3_2_1__armstrng)]).

fof(dh_c1_2_1_1__armstrng,definition,
    ( ( m1_subset_1(c1_2_1_1__armstrng,k1_zfmisc_1(k1_zfmisc_1(c2_2__armstrng)))
     => ( c1_2_1_1__armstrng = k2_xboole_0(c2_2_1__armstrng,k1_tarski(c1_2_1__armstrng))
       => r2_hidden(k8_setfam_1(c2_2__armstrng,c1_2_1_1__armstrng),c1_2__armstrng) ) )
   => ! [A] : 
        ( m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(c2_2__armstrng)))
       => ( A = k2_xboole_0(c2_2_1__armstrng,k1_tarski(c1_2_1__armstrng))
         => r2_hidden(k8_setfam_1(c2_2__armstrng,A),c1_2__armstrng) ) ) ),
    introduced(definition,[new_symbol(c1_2_1_1__armstrng),file(armstrng,c1_2_1_1__armstrng)]),
    [interesting(0.5),axiom,file(armstrng,c1_2_1_1__armstrng)]).

fof(e1_2_1_1__armstrng,assumption,(
    c1_2_1_1__armstrng = k2_xboole_0(c2_2_1__armstrng,k1_tarski(c1_2_1__armstrng)) ),
    introduced(assumption,[file(armstrng,e1_2_1_1__armstrng)]),
    [interesting(0.5),axiom,file(armstrng,e1_2_1_1__armstrng)]).

fof(t1_boole,theorem,(
    ! [A] : k2_xboole_0(A,k1_xboole_0) = A ),
    file(boole,t1_boole),
    [interesting(0.9),axiom,file(boole,t1_boole)]).

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

fof(fc10_finset_1,theorem,(
    ! [A,B] : 
      ( v1_finset_1(B)
     => v1_finset_1(k3_xboole_0(A,B)) ) ),
    file(finset_1,fc10_finset_1),
    [interesting(0.9),axiom,file(finset_1,fc10_finset_1)]).

fof(fc11_finset_1,theorem,(
    ! [A,B] : 
      ( v1_finset_1(A)
     => v1_finset_1(k3_xboole_0(A,B)) ) ),
    file(finset_1,fc11_finset_1),
    [interesting(0.9),axiom,file(finset_1,fc11_finset_1)]).

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

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

fof(commutativity_k4_subset_1,theorem,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k4_subset_1(A,B,C) = k4_subset_1(A,C,B) ) ),
    file(subset_1,k4_subset_1),
    [interesting(0.9),axiom,file(subset_1,k4_subset_1)]).

fof(idempotence_k4_subset_1,theorem,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k4_subset_1(A,B,B) = B ) ),
    file(subset_1,k4_subset_1),
    [interesting(0.9),axiom,file(subset_1,k4_subset_1)]).

fof(commutativity_k5_subset_1,theorem,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k5_subset_1(A,B,C) = k5_subset_1(A,C,B) ) ),
    file(subset_1,k5_subset_1),
    [interesting(0.9),axiom,file(subset_1,k5_subset_1)]).

fof(idempotence_k5_subset_1,theorem,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k5_subset_1(A,B,B) = B ) ),
    file(subset_1,k5_subset_1),
    [interesting(0.9),axiom,file(subset_1,k5_subset_1)]).

fof(redefinition_k4_subset_1,definition,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k4_subset_1(A,B,C) = k2_xboole_0(B,C) ) ),
    file(subset_1,k4_subset_1),
    [interesting(0.9),axiom,file(subset_1,k4_subset_1)]).

fof(redefinition_k5_subset_1,definition,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k5_subset_1(A,B,C) = k3_xboole_0(B,C) ) ),
    file(subset_1,k5_subset_1),
    [interesting(0.9),axiom,file(subset_1,k5_subset_1)]).

fof(dt_k3_xboole_0,axiom,(
    $true ),
    file(xboole_0,k3_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k3_xboole_0)]).

fof(dt_k4_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => m1_subset_1(k4_subset_1(A,B,C),k1_zfmisc_1(A)) ) ),
    file(subset_1,k4_subset_1),
    [interesting(0.9),axiom,file(subset_1,k4_subset_1)]).

fof(dt_k5_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => m1_subset_1(k5_subset_1(A,B,C),k1_zfmisc_1(A)) ) ),
    file(subset_1,k5_subset_1),
    [interesting(0.9),axiom,file(subset_1,k5_subset_1)]).

fof(dt_c1_2_1__armstrng,assumption,(
    $true ),
    introduced(assumption,[file(armstrng,c1_2_1__armstrng)]),
    [interesting(0.65),axiom,file(armstrng,c1_2_1__armstrng)]).

fof(dt_c1_2_1_1__armstrng,assumption,(
    m1_subset_1(c1_2_1_1__armstrng,k1_zfmisc_1(k1_zfmisc_1(c2_2__armstrng))) ),
    introduced(assumption,[file(armstrng,c1_2_1_1__armstrng)]),
    [interesting(0.5),axiom,file(armstrng,c1_2_1_1__armstrng)]).

fof(dt_c2_2_1__armstrng,assumption,(
    $true ),
    introduced(assumption,[file(armstrng,c2_2_1__armstrng)]),
    [interesting(0.65),axiom,file(armstrng,c2_2_1__armstrng)]).

fof(de_c2_2_1_1__armstrng,definition,(
    c2_2_1_1__armstrng = c1_2_1__armstrng ),
    introduced(definition,[new_symbol(c2_2_1_1__armstrng),file(armstrng,c2_2_1_1__armstrng)]),
    [interesting(0.5),axiom,file(armstrng,c2_2_1_1__armstrng)]).

fof(e2_2_1_1__armstrng,plain,(
    m1_subset_1(c1_2_1__armstrng,k1_zfmisc_1(c2_2__armstrng)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2_1__armstrng,dt_c2_2__armstrng,dt_c3_2__armstrng,e1_2_1__armstrng])],[cc1_finseq_1,cc2_funct_1,rc1_finseq_1,rc1_funct_1,rc1_margrel1,rc1_pboole,rc2_funct_1,rc3_finseq_1,rc3_funct_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,dt_k1_xboole_0,fc1_margrel1,fc1_xboole_0,fc2_finseq_1,t8_boole,reflexivity_r1_tarski,cc1_finset_1,cc1_funct_1,cc2_finset_1,rc1_finset_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,rc3_finset_1,rc4_finset_1,t2_subset,t5_subset,t6_boole,antisymmetry_r2_hidden,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,dt_c1_2_1__armstrng,dt_c2_2__armstrng,dt_c3_2__armstrng,fc1_subset_1,t1_subset,t3_subset,t4_subset,t7_boole,e1_2_1__armstrng]),
    [interesting(0.5),file(armstrng,e2_2_1_1__armstrng),[file(armstrng,e2_2_1_1__armstrng)]]).

fof(dt_c2_2_1_1__armstrng,plain,(
    m1_subset_1(c2_2_1_1__armstrng,k1_zfmisc_1(c2_2__armstrng)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2_1__armstrng,dt_c2_2__armstrng,dt_c3_2__armstrng,e1_2_1__armstrng])],[cc1_finseq_1,cc2_funct_1,rc1_finseq_1,rc1_funct_1,rc1_margrel1,rc1_pboole,rc2_funct_1,rc3_finseq_1,rc3_funct_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,antisymmetry_r2_hidden,dt_k1_xboole_0,cc2_finset_1,fc1_margrel1,fc1_xboole_0,fc2_finseq_1,rc1_finset_1,rc3_finset_1,rc4_finset_1,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,cc1_finset_1,cc1_funct_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,dt_c1_2_1__armstrng,dt_c2_2__armstrng,fc1_subset_1,t3_subset,de_c2_2_1_1__armstrng,e2_2_1_1__armstrng]),
    [interesting(0.5),file(armstrng,c2_2_1_1__armstrng),[file(armstrng,c2_2_1_1__armstrng)]]).

fof(de_c3_2_1_1__armstrng,definition,(
    c3_2_1_1__armstrng = c2_2_1__armstrng ),
    introduced(definition,[new_symbol(c3_2_1_1__armstrng),file(armstrng,c3_2_1_1__armstrng)]),
    [interesting(0.5),axiom,file(armstrng,c3_2_1_1__armstrng)]).

fof(t1_xboole_1,theorem,(
    ! [A,B,C] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(B,C) )
     => r1_tarski(A,C) ) ),
    file(xboole_1,t1_xboole_1),
    [interesting(0.9),axiom,file(xboole_1,t1_xboole_1)]).

fof(e3_2_1_1__armstrng,plain,(
    r1_tarski(c2_2_1__armstrng,k1_zfmisc_1(c2_2__armstrng)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_2__armstrng,dt_c2_2_1__armstrng,dt_c3_2__armstrng,e2_2_1__armstrng])],[cc1_finseq_1,cc2_funct_1,rc1_finseq_1,rc1_funct_1,rc1_margrel1,rc1_pboole,rc2_funct_1,rc3_finseq_1,rc3_funct_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,antisymmetry_r2_hidden,dt_k1_xboole_0,fc1_margrel1,fc1_xboole_0,fc2_finseq_1,t1_subset,t4_subset,t5_subset,t8_boole,existence_m1_subset_1,dt_m1_subset_1,cc1_finset_1,cc1_funct_1,cc2_finset_1,rc1_finset_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,rc3_finset_1,rc4_finset_1,t2_subset,t6_boole,t7_boole,reflexivity_r1_tarski,dt_k1_zfmisc_1,dt_c2_2__armstrng,dt_c2_2_1__armstrng,dt_c3_2__armstrng,fc1_subset_1,t3_subset,e2_2_1__armstrng,t1_xboole_1]),
    [interesting(0.5),file(armstrng,e3_2_1_1__armstrng),[file(armstrng,e3_2_1_1__armstrng)]]).

fof(e4_2_1_1__armstrng,plain,(
    m1_subset_1(c2_2_1__armstrng,k1_zfmisc_1(k1_zfmisc_1(c2_2__armstrng))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_2__armstrng,dt_c2_2_1__armstrng,dt_c3_2__armstrng,e2_2_1__armstrng])],[cc1_finseq_1,cc2_funct_1,rc1_finseq_1,rc1_funct_1,rc1_margrel1,rc1_pboole,rc2_funct_1,rc3_finseq_1,rc3_funct_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,antisymmetry_r2_hidden,dt_k1_xboole_0,cc2_finset_1,fc1_margrel1,fc1_xboole_0,fc2_finseq_1,rc1_finset_1,rc3_finset_1,rc4_finset_1,t1_subset,t4_subset,t5_subset,t8_boole,cc1_finset_1,cc1_funct_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,t2_subset,t6_boole,t7_boole,reflexivity_r1_tarski,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,dt_c2_2__armstrng,dt_c2_2_1__armstrng,fc1_subset_1,t3_subset,e3_2_1_1__armstrng]),
    [interesting(0.5),file(armstrng,e4_2_1_1__armstrng),[file(armstrng,e4_2_1_1__armstrng)]]).

fof(dt_c3_2_1_1__armstrng,plain,(
    m1_subset_1(c3_2_1_1__armstrng,k1_zfmisc_1(k1_zfmisc_1(c2_2__armstrng))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_2__armstrng,dt_c2_2_1__armstrng,dt_c3_2__armstrng,e2_2_1__armstrng])],[cc1_finseq_1,cc2_funct_1,rc1_finseq_1,rc1_funct_1,rc1_margrel1,rc1_pboole,rc2_funct_1,rc3_finseq_1,rc3_funct_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,antisymmetry_r2_hidden,dt_k1_xboole_0,cc2_finset_1,fc1_margrel1,fc1_xboole_0,fc2_finseq_1,rc1_finset_1,rc3_finset_1,rc4_finset_1,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,cc1_finset_1,cc1_funct_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,dt_c2_2__armstrng,dt_c2_2_1__armstrng,fc1_subset_1,t3_subset,de_c3_2_1_1__armstrng,e4_2_1_1__armstrng]),
    [interesting(0.5),file(armstrng,c3_2_1_1__armstrng),[file(armstrng,c3_2_1_1__armstrng)]]).

fof(de_c4_2_1_1__armstrng,definition,(
    c4_2_1_1__armstrng = k1_tarski(c1_2_1__armstrng) ),
    introduced(definition,[new_symbol(c4_2_1_1__armstrng),file(armstrng,c4_2_1_1__armstrng)]),
    [interesting(0.5),axiom,file(armstrng,c4_2_1_1__armstrng)]).

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(e5_2_1_1__armstrng,plain,(
    r1_tarski(k1_tarski(c1_2_1__armstrng),k1_zfmisc_1(c2_2__armstrng)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2_1__armstrng,dt_c2_2__armstrng,dt_c3_2__armstrng,e1_2_1__armstrng])],[cc1_altcat_1,cc1_fraenkel,rc1_fraenkel,cc1_finseq_1,cc2_funct_1,fc2_altcat_1,rc1_finseq_1,rc1_funct_1,rc1_margrel1,rc1_pboole,rc2_funct_1,rc3_finseq_1,rc3_funct_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,dt_k1_xboole_0,fc1_margrel1,fc1_xboole_0,fc2_finseq_1,t8_boole,existence_m1_subset_1,dt_m1_subset_1,cc1_finset_1,cc1_funct_1,cc2_finset_1,rc1_finset_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,rc3_finset_1,rc4_finset_1,t2_subset,t4_subset,t5_subset,t6_boole,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_tarski,dt_k1_zfmisc_1,dt_c1_2_1__armstrng,dt_c2_2__armstrng,dt_c3_2__armstrng,fc1_finset_1,fc1_subset_1,fc2_subset_1,t1_subset,t3_subset,t7_boole,e1_2_1__armstrng,t37_zfmisc_1]),
    [interesting(0.5),file(armstrng,e5_2_1_1__armstrng),[file(armstrng,e5_2_1_1__armstrng)]]).

fof(e6_2_1_1__armstrng,plain,(
    m1_subset_1(k1_tarski(c1_2_1__armstrng),k1_zfmisc_1(k1_zfmisc_1(c2_2__armstrng))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2_1__armstrng,dt_c2_2__armstrng,dt_c3_2__armstrng,e1_2_1__armstrng])],[cc1_altcat_1,cc1_fraenkel,rc1_fraenkel,cc1_finseq_1,cc2_funct_1,fc2_altcat_1,rc1_finseq_1,rc1_funct_1,rc1_margrel1,rc1_pboole,rc2_funct_1,rc3_finseq_1,rc3_funct_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,antisymmetry_r2_hidden,dt_k1_xboole_0,fc1_margrel1,fc1_xboole_0,fc2_finseq_1,t1_subset,t4_subset,t5_subset,t8_boole,cc1_finset_1,cc1_funct_1,cc2_finset_1,rc1_finset_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,rc3_finset_1,rc4_finset_1,t2_subset,t6_boole,t7_boole,reflexivity_r1_tarski,existence_m1_subset_1,dt_k1_tarski,dt_k1_zfmisc_1,dt_m1_subset_1,dt_c1_2_1__armstrng,dt_c2_2__armstrng,fc1_finset_1,fc1_subset_1,fc2_subset_1,t3_subset,e5_2_1_1__armstrng]),
    [interesting(0.5),file(armstrng,e6_2_1_1__armstrng),[file(armstrng,e6_2_1_1__armstrng)]]).

fof(dt_c4_2_1_1__armstrng,plain,(
    m1_subset_1(c4_2_1_1__armstrng,k1_zfmisc_1(k1_zfmisc_1(c2_2__armstrng))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2_1__armstrng,dt_c2_2__armstrng,dt_c3_2__armstrng,e1_2_1__armstrng])],[cc1_altcat_1,cc1_fraenkel,rc1_fraenkel,cc1_finseq_1,cc2_funct_1,fc2_altcat_1,rc1_finseq_1,rc1_funct_1,rc1_margrel1,rc1_pboole,rc2_funct_1,rc3_finseq_1,rc3_funct_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,antisymmetry_r2_hidden,dt_k1_xboole_0,fc1_margrel1,fc1_xboole_0,fc2_finseq_1,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,cc1_finset_1,cc1_funct_1,cc2_finset_1,rc1_finset_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,rc3_finset_1,rc4_finset_1,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_subset_1,dt_k1_tarski,dt_k1_zfmisc_1,dt_m1_subset_1,dt_c1_2_1__armstrng,dt_c2_2__armstrng,fc1_finset_1,fc1_subset_1,fc2_subset_1,t3_subset,de_c4_2_1_1__armstrng,e6_2_1_1__armstrng]),
    [interesting(0.5),file(armstrng,c4_2_1_1__armstrng),[file(armstrng,c4_2_1_1__armstrng)]]).

fof(t8_mssubfam,theorem,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ! [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A)))
         => ! [D] : 
              ( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(A)))
             => ( B = k4_subset_1(k1_zfmisc_1(A),C,D)
               => k8_setfam_1(A,B) = k5_subset_1(A,k8_setfam_1(A,C),k8_setfam_1(A,D)) ) ) ) ) ),
    file(mssubfam,t8_mssubfam),
    [interesting(0.9),axiom,file(mssubfam,t8_mssubfam)]).

fof(e1_2_1_1_1__armstrng,plain,(
    k8_setfam_1(c2_2__armstrng,k4_subset_1(k1_zfmisc_1(c2_2__armstrng),c3_2_1_1__armstrng,c4_2_1_1__armstrng)) = k5_subset_1(c2_2__armstrng,k8_setfam_1(c2_2__armstrng,c3_2_1_1__armstrng),k8_setfam_1(c2_2__armstrng,c4_2_1_1__armstrng)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_2_1__armstrng,e2_2_1__armstrng,dt_c1_2_1__armstrng,dt_c2_2__armstrng,dt_c3_2__armstrng,e1_2_1__armstrng])],[cc1_altcat_1,cc1_fraenkel,rc1_fraenkel,cc1_finseq_1,cc2_funct_1,fc2_altcat_1,rc1_finseq_1,rc1_funct_1,rc1_margrel1,rc1_pboole,rc2_funct_1,rc3_finseq_1,rc3_funct_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,antisymmetry_r2_hidden,dt_k1_xboole_0,cc2_finset_1,fc10_finset_1,fc11_finset_1,fc1_margrel1,fc1_xboole_0,fc2_finseq_1,fc9_finset_1,rc1_finset_1,rc3_finset_1,rc4_finset_1,t1_boole,t1_subset,t2_boole,t4_subset,t5_subset,commutativity_k2_xboole_0,idempotence_k2_xboole_0,commutativity_k3_xboole_0,idempotence_k3_xboole_0,reflexivity_r1_tarski,dt_k1_tarski,dt_k2_xboole_0,dt_k3_xboole_0,dt_c1_2_1__armstrng,dt_c2_2_1__armstrng,cc1_finset_1,cc1_funct_1,fc1_finset_1,fc2_subset_1,fc2_xboole_0,fc3_xboole_0,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k4_subset_1,idempotence_k4_subset_1,commutativity_k5_subset_1,idempotence_k5_subset_1,existence_m1_subset_1,redefinition_k4_subset_1,redefinition_k5_subset_1,dt_k1_zfmisc_1,dt_k4_subset_1,dt_k5_subset_1,dt_k8_setfam_1,dt_m1_subset_1,dt_c2_2__armstrng,dt_c3_2_1_1__armstrng,dt_c4_2_1_1__armstrng,de_c3_2_1_1__armstrng,de_c4_2_1_1__armstrng,fc1_subset_1,t3_subset,t8_mssubfam]),
    [interesting(0.35),file(armstrng,e1_2_1_1_1__armstrng),[file(armstrng,e1_2_1_1_1__armstrng)]]).

fof(t9_mssubfam,theorem,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ! [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(A))
         => ( B = k1_tarski(C)
           => k8_setfam_1(A,B) = C ) ) ) ),
    file(mssubfam,t9_mssubfam),
    [interesting(0.9),axiom,file(mssubfam,t9_mssubfam)]).

fof(e2_2_1_1_1__armstrng,plain,(
    k5_subset_1(c2_2__armstrng,k8_setfam_1(c2_2__armstrng,c3_2_1_1__armstrng),k8_setfam_1(c2_2__armstrng,c4_2_1_1__armstrng)) = k5_subset_1(c2_2__armstrng,k8_setfam_1(c2_2__armstrng,c3_2_1_1__armstrng),c2_2_1_1__armstrng) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_2_1__armstrng,e2_2_1__armstrng,dt_c1_2_1__armstrng,dt_c2_2__armstrng,dt_c3_2__armstrng,e1_2_1__armstrng])],[cc1_altcat_1,cc1_fraenkel,rc1_fraenkel,cc1_finseq_1,cc2_funct_1,fc2_altcat_1,rc1_finseq_1,rc1_funct_1,rc1_margrel1,rc1_pboole,rc2_funct_1,rc3_finseq_1,rc3_funct_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,antisymmetry_r2_hidden,dt_k1_xboole_0,fc1_margrel1,fc1_xboole_0,fc2_finseq_1,t1_subset,t2_boole,t4_subset,t5_subset,commutativity_k3_xboole_0,idempotence_k3_xboole_0,reflexivity_r1_tarski,dt_k3_xboole_0,dt_c1_2_1__armstrng,dt_c2_2_1__armstrng,cc1_finset_1,cc1_funct_1,cc2_finset_1,fc10_finset_1,fc11_finset_1,rc1_finset_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,rc3_finset_1,rc4_finset_1,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k5_subset_1,idempotence_k5_subset_1,existence_m1_subset_1,redefinition_k5_subset_1,dt_k1_tarski,dt_k1_zfmisc_1,dt_k5_subset_1,dt_k8_setfam_1,dt_m1_subset_1,dt_c2_2__armstrng,dt_c2_2_1_1__armstrng,dt_c3_2_1_1__armstrng,dt_c4_2_1_1__armstrng,de_c2_2_1_1__armstrng,de_c3_2_1_1__armstrng,de_c4_2_1_1__armstrng,fc1_finset_1,fc1_subset_1,fc2_subset_1,t3_subset,t9_mssubfam]),
    [interesting(0.35),file(armstrng,e2_2_1_1_1__armstrng),[file(armstrng,e2_2_1_1_1__armstrng)]]).

fof(e8_2_1_1__armstrng,plain,(
    k8_setfam_1(c2_2__armstrng,k4_subset_1(k1_zfmisc_1(c2_2__armstrng),c3_2_1_1__armstrng,c4_2_1_1__armstrng)) = k5_subset_1(c2_2__armstrng,k8_setfam_1(c2_2__armstrng,c3_2_1_1__armstrng),c2_2_1_1__armstrng) ),
    inference(iterative_eq,[status(thm),assumptions([dt_c2_2_1__armstrng,e2_2_1__armstrng,dt_c1_2_1__armstrng,dt_c2_2__armstrng,dt_c3_2__armstrng,e1_2_1__armstrng])],[e1_2_1_1_1__armstrng,e2_2_1_1_1__armstrng]),
    [interesting(0.5),file(armstrng,e8_2_1_1__armstrng),[file(armstrng,e8_2_1_1__armstrng)]]).

fof(e7_2_1_1__armstrng,plain,(
    r2_hidden(k8_setfam_1(c2_2__armstrng,c3_2_1_1__armstrng),c1_2__armstrng) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2__armstrng,dt_c2_2__armstrng,dt_c2_2_1__armstrng,dt_c3_2__armstrng,e2_2_1__armstrng,e3_2_1__armstrng])],[cc1_finseq_1,cc2_funct_1,rc1_finseq_1,rc1_funct_1,rc1_margrel1,rc1_pboole,rc2_funct_1,rc3_finseq_1,rc3_funct_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,dt_k1_xboole_0,cc2_finset_1,fc1_margrel1,fc1_xboole_0,fc2_finseq_1,rc1_finset_1,rc3_finset_1,rc4_finset_1,reflexivity_r1_tarski,cc1_finset_1,cc1_funct_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,t2_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k8_setfam_1,dt_m1_subset_1,dt_c1_2__armstrng,dt_c2_2__armstrng,dt_c2_2_1__armstrng,dt_c3_2_1_1__armstrng,de_c3_2_1_1__armstrng,fc1_subset_1,t1_subset,t3_subset,t4_subset,t7_boole,e3_2_1__armstrng]),
    [interesting(0.5),file(armstrng,e7_2_1_1__armstrng),[file(armstrng,e7_2_1_1__armstrng)]]).

fof(d2_finsub_1,definition,(
    ! [A] : 
      ( v2_finsub_1(A)
    <=> ! [B,C] : 
          ( ( r2_hidden(B,A)
            & r2_hidden(C,A) )
         => r2_hidden(k3_xboole_0(B,C),A) ) ) ),
    file(finsub_1,d2_finsub_1),
    [interesting(0.9),axiom,file(finsub_1,d2_finsub_1)]).

fof(e9_2_1_1__armstrng,plain,(
    r2_hidden(k8_setfam_1(c2_2__armstrng,c1_2_1_1__armstrng),c1_2__armstrng) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2_1_1__armstrng,dt_c1_2_1__armstrng,e1_2__armstrng,e3_2__armstrng,e1_2_1__armstrng,e1_2_1_1__armstrng,dt_c1_2__armstrng,dt_c2_2__armstrng,dt_c2_2_1__armstrng,dt_c3_2__armstrng,e2_2_1__armstrng,e3_2_1__armstrng])],[cc1_altcat_1,cc1_fraenkel,rc1_fraenkel,cc1_finseq_1,cc2_funct_1,fc2_altcat_1,rc1_finseq_1,rc1_funct_1,rc1_margrel1,rc1_pboole,rc2_funct_1,rc3_finseq_1,rc3_funct_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,dt_k1_xboole_0,fc1_margrel1,fc1_xboole_0,fc2_finseq_1,t1_boole,t2_boole,existence_m1_subset_1,dt_m1_subset_1,cc1_finset_1,cc1_funct_1,cc2_finset_1,fc10_finset_1,fc11_finset_1,fc2_xboole_0,fc3_xboole_0,fc9_finset_1,rc1_finset_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,rc3_finset_1,rc4_finset_1,t2_subset,t4_subset,t5_subset,t6_boole,t8_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,commutativity_k3_xboole_0,idempotence_k3_xboole_0,commutativity_k4_subset_1,idempotence_k4_subset_1,commutativity_k5_subset_1,idempotence_k5_subset_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,redefinition_k4_subset_1,redefinition_k5_subset_1,dt_k1_tarski,dt_k1_zfmisc_1,dt_k2_xboole_0,dt_k3_xboole_0,dt_k4_subset_1,dt_k5_subset_1,dt_k8_setfam_1,dt_c1_2__armstrng,dt_c1_2_1__armstrng,dt_c1_2_1_1__armstrng,dt_c2_2__armstrng,dt_c2_2_1__armstrng,dt_c2_2_1_1__armstrng,dt_c3_2__armstrng,dt_c3_2_1_1__armstrng,dt_c4_2_1_1__armstrng,de_c2_2_1_1__armstrng,de_c3_2_1_1__armstrng,de_c4_2_1_1__armstrng,fc1_finset_1,fc1_subset_1,fc2_subset_1,t1_subset,t3_subset,t7_boole,e8_2_1_1__armstrng,e1_2__armstrng,e3_2__armstrng,e1_2_1__armstrng,e1_2_1_1__armstrng,e7_2_1_1__armstrng,d2_finsub_1]),
    [interesting(0.5),file(armstrng,e9_2_1_1__armstrng),[file(armstrng,e9_2_1_1__armstrng)]]).

fof(i3_2_1_1__armstrng,theorem,(
    $true ),
    introduced(tautology,[file(armstrng,i3_2_1_1__armstrng)]),
    [interesting(0.5),trivial,file(armstrng,i3_2_1_1__armstrng)]).

fof(i2_2_1_1__armstrng,plain,(
    r2_hidden(k8_setfam_1(c2_2__armstrng,c1_2_1_1__armstrng),c1_2__armstrng) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_2_1_1__armstrng,dt_c1_2_1__armstrng,e1_2__armstrng,e3_2__armstrng,e1_2_1__armstrng,e1_2_1_1__armstrng,dt_c1_2__armstrng,dt_c2_2__armstrng,dt_c2_2_1__armstrng,dt_c3_2__armstrng,e2_2_1__armstrng,e3_2_1__armstrng])],[e9_2_1_1__armstrng,i3_2_1_1__armstrng]),
    [interesting(0.5),file(armstrng,i2_2_1_1__armstrng),[file(armstrng,i2_2_1_1__armstrng)]]).

fof(i1_2_1_1__armstrng,plain,
    ( c1_2_1_1__armstrng = k2_xboole_0(c2_2_1__armstrng,k1_tarski(c1_2_1__armstrng))
   => r2_hidden(k8_setfam_1(c2_2__armstrng,c1_2_1_1__armstrng),c1_2__armstrng) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_2_1_1__armstrng,dt_c1_2_1__armstrng,e1_2__armstrng,e3_2__armstrng,e1_2_1__armstrng,dt_c1_2__armstrng,dt_c2_2__armstrng,dt_c2_2_1__armstrng,dt_c3_2__armstrng,e2_2_1__armstrng,e3_2_1__armstrng]),discharge_asm(discharge,[e1_2_1_1__armstrng])],[e1_2_1_1__armstrng,i2_2_1_1__armstrng]),
    [interesting(0.5),file(armstrng,i1_2_1_1__armstrng),[file(armstrng,i1_2_1_1__armstrng)]]).

fof(i1_2_1_1_tmp__armstrng,plain,
    ( m1_subset_1(c1_2_1_1__armstrng,k1_zfmisc_1(k1_zfmisc_1(c2_2__armstrng)))
   => ( c1_2_1_1__armstrng = k2_xboole_0(c2_2_1__armstrng,k1_tarski(c1_2_1__armstrng))
     => r2_hidden(k8_setfam_1(c2_2__armstrng,c1_2_1_1__armstrng),c1_2__armstrng) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_2_1__armstrng,e1_2__armstrng,e3_2__armstrng,e1_2_1__armstrng,dt_c1_2__armstrng,dt_c2_2__armstrng,dt_c2_2_1__armstrng,dt_c3_2__armstrng,e2_2_1__armstrng,e3_2_1__armstrng]),discharge_asm(discharge,[dt_c1_2_1_1__armstrng])],[dt_c1_2_1_1__armstrng,i1_2_1_1__armstrng]),
    [interesting(0.65),e4_2_1__armstrng]).

fof(e4_2_1__armstrng,plain,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(c2_2__armstrng)))
     => ( A = k2_xboole_0(c2_2_1__armstrng,k1_tarski(c1_2_1__armstrng))
       => r2_hidden(k8_setfam_1(c2_2__armstrng,A),c1_2__armstrng) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_2_1__armstrng,e1_2__armstrng,e3_2__armstrng,e1_2_1__armstrng,dt_c1_2__armstrng,dt_c2_2__armstrng,dt_c2_2_1__armstrng,dt_c3_2__armstrng,e2_2_1__armstrng,e3_2_1__armstrng])],[i1_2_1_1_tmp__armstrng,dh_c1_2_1_1__armstrng]),
    [interesting(0.65),file(armstrng,e4_2_1__armstrng),[file(armstrng,e4_2_1__armstrng)]]).

fof(i4_2_1__armstrng,theorem,(
    $true ),
    introduced(tautology,[file(armstrng,i4_2_1__armstrng)]),
    [interesting(0.65),trivial,file(armstrng,i4_2_1__armstrng)]).

fof(i3_2_1__armstrng,plain,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(c2_2__armstrng)))
     => ( A = k2_xboole_0(c2_2_1__armstrng,k1_tarski(c1_2_1__armstrng))
       => r2_hidden(k8_setfam_1(c2_2__armstrng,A),c1_2__armstrng) ) ) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_2_1__armstrng,e1_2__armstrng,e3_2__armstrng,e1_2_1__armstrng,dt_c1_2__armstrng,dt_c2_2__armstrng,dt_c2_2_1__armstrng,dt_c3_2__armstrng,e2_2_1__armstrng,e3_2_1__armstrng])],[e4_2_1__armstrng,i4_2_1__armstrng]),
    [interesting(0.65),file(armstrng,i3_2_1__armstrng),[file(armstrng,i3_2_1__armstrng)]]).

fof(i2_2_1__armstrng,plain,
    ( ( r2_hidden(c1_2_1__armstrng,c3_2__armstrng)
      & r1_tarski(c2_2_1__armstrng,c3_2__armstrng)
      & ! [A] : 
          ( m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(c2_2__armstrng)))
         => ( A = c2_2_1__armstrng
           => r2_hidden(k8_setfam_1(c2_2__armstrng,A),c1_2__armstrng) ) ) )
   => ! [A] : 
        ( m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(c2_2__armstrng)))
       => ( A = k2_xboole_0(c2_2_1__armstrng,k1_tarski(c1_2_1__armstrng))
         => r2_hidden(k8_setfam_1(c2_2__armstrng,A),c1_2__armstrng) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_2_1__armstrng,e1_2__armstrng,e3_2__armstrng,dt_c1_2__armstrng,dt_c2_2__armstrng,dt_c2_2_1__armstrng,dt_c3_2__armstrng]),discharge_asm(discharge,[e1_2_1__armstrng,e2_2_1__armstrng,e3_2_1__armstrng])],[e1_2_1__armstrng,e2_2_1__armstrng,e3_2_1__armstrng,i3_2_1__armstrng]),
    [interesting(0.65),file(armstrng,i2_2_1__armstrng),[file(armstrng,i2_2_1__armstrng)]]).

fof(i2_2_1_tmp__armstrng,plain,
    ( ( r2_hidden(c1_2_1__armstrng,c3_2__armstrng)
      & r1_tarski(c2_2_1__armstrng,c3_2__armstrng)
      & ! [A] : 
          ( m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(c2_2__armstrng)))
         => ( A = c2_2_1__armstrng
           => r2_hidden(k8_setfam_1(c2_2__armstrng,A),c1_2__armstrng) ) ) )
   => ! [A] : 
        ( m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(c2_2__armstrng)))
       => ( A = k2_xboole_0(c2_2_1__armstrng,k1_tarski(c1_2_1__armstrng))
         => r2_hidden(k8_setfam_1(c2_2__armstrng,A),c1_2__armstrng) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_2_1__armstrng,e1_2__armstrng,e3_2__armstrng,dt_c1_2__armstrng,dt_c2_2__armstrng,dt_c3_2__armstrng]),discharge_asm(discharge,[dt_c2_2_1__armstrng])],[dt_c2_2_1__armstrng,i2_2_1__armstrng]),
    [interesting(0.65),i1_2_1__armstrng]).

fof(i1_2_1__armstrng,plain,(
    ! [A] : 
      ( ( r2_hidden(c1_2_1__armstrng,c3_2__armstrng)
        & r1_tarski(A,c3_2__armstrng)
        & ! [B] : 
            ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(c2_2__armstrng)))
           => ( B = A
             => r2_hidden(k8_setfam_1(c2_2__armstrng,B),c1_2__armstrng) ) ) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(c2_2__armstrng)))
         => ( B = k2_xboole_0(A,k1_tarski(c1_2_1__armstrng))
           => r2_hidden(k8_setfam_1(c2_2__armstrng,B),c1_2__armstrng) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_2_1__armstrng,e1_2__armstrng,e3_2__armstrng,dt_c1_2__armstrng,dt_c2_2__armstrng,dt_c3_2__armstrng])],[i2_2_1_tmp__armstrng,dh_c2_2_1__armstrng]),
    [interesting(0.65),file(armstrng,i1_2_1__armstrng),[file(armstrng,i1_2_1__armstrng)]]).

fof(i1_2_1_tmp__armstrng,plain,(
    ! [A] : 
      ( ( r2_hidden(c1_2_1__armstrng,c3_2__armstrng)
        & r1_tarski(A,c3_2__armstrng)
        & ! [B] : 
            ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(c2_2__armstrng)))
           => ( B = A
             => r2_hidden(k8_setfam_1(c2_2__armstrng,B),c1_2__armstrng) ) ) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(c2_2__armstrng)))
         => ( B = k2_xboole_0(A,k1_tarski(c1_2_1__armstrng))
           => r2_hidden(k8_setfam_1(c2_2__armstrng,B),c1_2__armstrng) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([e1_2__armstrng,e3_2__armstrng,dt_c1_2__armstrng,dt_c2_2__armstrng,dt_c3_2__armstrng]),discharge_asm(discharge,[dt_c1_2_1__armstrng])],[dt_c1_2_1__armstrng,i1_2_1__armstrng]),
    [interesting(0.8),e6_2__armstrng]).

fof(e6_2__armstrng,plain,(
    ! [A,B] : 
      ( ( r2_hidden(A,c3_2__armstrng)
        & r1_tarski(B,c3_2__armstrng)
        & ! [C] : 
            ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(c2_2__armstrng)))
           => ( C = B
             => r2_hidden(k8_setfam_1(c2_2__armstrng,C),c1_2__armstrng) ) ) )
     => ! [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(c2_2__armstrng)))
         => ( C = k2_xboole_0(B,k1_tarski(A))
           => r2_hidden(k8_setfam_1(c2_2__armstrng,C),c1_2__armstrng) ) ) ) ),
    inference(let,[status(thm),assumptions([e1_2__armstrng,e3_2__armstrng,dt_c1_2__armstrng,dt_c2_2__armstrng,dt_c3_2__armstrng])],[i1_2_1_tmp__armstrng,dh_c1_2_1__armstrng]),
    [interesting(0.8),file(armstrng,e6_2__armstrng),[file(armstrng,e6_2__armstrng)]]).

fof(e7_2__armstrng,plain,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(c2_2__armstrng)))
     => ( A = c3_2__armstrng
       => r2_hidden(k8_setfam_1(c2_2__armstrng,A),c1_2__armstrng) ) ) ),
    inference(mizar_from,[status(thm),assumptions([e2_2__armstrng,e1_2__armstrng,e3_2__armstrng,dt_c1_2__armstrng,dt_c2_2__armstrng,dt_c3_2__armstrng])],[cc1_altcat_1,cc1_fraenkel,rc1_fraenkel,cc1_finseq_1,cc1_finset_1,cc1_funct_1,cc2_funct_1,fc2_altcat_1,fc2_xboole_0,fc3_xboole_0,rc1_finseq_1,rc1_finset_1,rc1_funct_1,rc1_margrel1,rc1_pboole,rc1_subset_1,rc1_xboole_0,rc2_funct_1,rc2_subset_1,rc2_xboole_0,rc3_finseq_1,rc3_finset_1,rc3_funct_1,rc4_finset_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,commutativity_k2_xboole_0,idempotence_k2_xboole_0,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_xboole_0,dt_k8_setfam_1,dt_m1_subset_1,dt_c1_2__armstrng,dt_c2_2__armstrng,dt_c3_2__armstrng,cc2_finset_1,fc1_finset_1,fc1_margrel1,fc1_subset_1,fc1_xboole_0,fc2_finseq_1,fc2_subset_1,fc9_finset_1,s2_finset_1__e7_2__armstrng,e4_2__armstrng,e5_2__armstrng,e6_2__armstrng]),
    [interesting(0.8),file(armstrng,e7_2__armstrng),[file(armstrng,e7_2__armstrng)]]).

fof(e8_2__armstrng,plain,(
    r2_hidden(k8_setfam_1(c2_2__armstrng,c3_2__armstrng),c1_2__armstrng) ),
    inference(mizar_by,[status(thm),assumptions([e2_2__armstrng,e1_2__armstrng,e3_2__armstrng,dt_c1_2__armstrng,dt_c2_2__armstrng,dt_c3_2__armstrng])],[cc1_finseq_1,cc2_funct_1,rc1_finseq_1,rc1_funct_1,rc1_margrel1,rc1_pboole,rc2_funct_1,rc3_finseq_1,rc3_funct_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,dt_k1_xboole_0,fc1_margrel1,fc1_xboole_0,fc2_finseq_1,reflexivity_r1_tarski,cc1_finset_1,cc1_funct_1,cc2_finset_1,rc1_finset_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,rc3_finset_1,rc4_finset_1,t2_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k8_setfam_1,dt_m1_subset_1,dt_c1_2__armstrng,dt_c2_2__armstrng,dt_c3_2__armstrng,fc1_subset_1,t1_subset,t3_subset,t4_subset,t7_boole,e7_2__armstrng]),
    [interesting(0.8),file(armstrng,e8_2__armstrng),[file(armstrng,e8_2__armstrng)]]).

fof(i6_2__armstrng,theorem,(
    $true ),
    introduced(tautology,[file(armstrng,i6_2__armstrng)]),
    [interesting(0.8),trivial,file(armstrng,i6_2__armstrng)]).

fof(i5_2__armstrng,plain,(
    r2_hidden(k8_setfam_1(c2_2__armstrng,c3_2__armstrng),c1_2__armstrng) ),
    inference(conclusion,[status(thm),assumptions([e2_2__armstrng,e1_2__armstrng,e3_2__armstrng,dt_c1_2__armstrng,dt_c2_2__armstrng,dt_c3_2__armstrng])],[e8_2__armstrng,i6_2__armstrng]),
    [interesting(0.8),file(armstrng,i5_2__armstrng),[file(armstrng,i5_2__armstrng)]]).

fof(i4_2__armstrng,plain,
    ( ( r2_hidden(c2_2__armstrng,c1_2__armstrng)
      & r1_tarski(c3_2__armstrng,c1_2__armstrng) )
   => r2_hidden(k8_setfam_1(c2_2__armstrng,c3_2__armstrng),c1_2__armstrng) ),
    inference(discharge_asm,[status(thm),assumptions([e1_2__armstrng,dt_c1_2__armstrng,dt_c2_2__armstrng,dt_c3_2__armstrng]),discharge_asm(discharge,[e2_2__armstrng,e3_2__armstrng])],[e2_2__armstrng,e3_2__armstrng,i5_2__armstrng]),
    [interesting(0.8),file(armstrng,i4_2__armstrng),[file(armstrng,i4_2__armstrng)]]).

fof(i4_2_tmp__armstrng,plain,
    ( ( v1_finset_1(c3_2__armstrng)
      & m1_subset_1(c3_2__armstrng,k1_zfmisc_1(k1_zfmisc_1(c2_2__armstrng))) )
   => ( ( r2_hidden(c2_2__armstrng,c1_2__armstrng)
        & r1_tarski(c3_2__armstrng,c1_2__armstrng) )
     => r2_hidden(k8_setfam_1(c2_2__armstrng,c3_2__armstrng),c1_2__armstrng) ) ),
    inference(discharge_asm,[status(thm),assumptions([e1_2__armstrng,dt_c1_2__armstrng,dt_c2_2__armstrng]),discharge_asm(discharge,[dt_c3_2__armstrng])],[dt_c3_2__armstrng,i4_2__armstrng]),
    [interesting(0.8),i3_2__armstrng]).

fof(i3_2__armstrng,plain,(
    ! [A] : 
      ( ( v1_finset_1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(c2_2__armstrng))) )
     => ( ( r2_hidden(c2_2__armstrng,c1_2__armstrng)
          & r1_tarski(A,c1_2__armstrng) )
       => r2_hidden(k8_setfam_1(c2_2__armstrng,A),c1_2__armstrng) ) ) ),
    inference(let,[status(thm),assumptions([e1_2__armstrng,dt_c1_2__armstrng,dt_c2_2__armstrng])],[i4_2_tmp__armstrng,dh_c3_2__armstrng]),
    [interesting(0.8),file(armstrng,i3_2__armstrng),[file(armstrng,i3_2__armstrng)]]).

fof(i3_2_tmp__armstrng,plain,(
    ! [A] : 
      ( ( v1_finset_1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(c2_2__armstrng))) )
     => ( ( r2_hidden(c2_2__armstrng,c1_2__armstrng)
          & r1_tarski(A,c1_2__armstrng) )
       => r2_hidden(k8_setfam_1(c2_2__armstrng,A),c1_2__armstrng) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([e1_2__armstrng,dt_c1_2__armstrng]),discharge_asm(discharge,[dt_c2_2__armstrng])],[dt_c2_2__armstrng,i3_2__armstrng]),
    [interesting(0.8),i2_2__armstrng]).

fof(i2_2__armstrng,plain,(
    ! [A,B] : 
      ( ( v1_finset_1(B)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
     => ( ( r2_hidden(A,c1_2__armstrng)
          & r1_tarski(B,c1_2__armstrng) )
       => r2_hidden(k8_setfam_1(A,B),c1_2__armstrng) ) ) ),
    inference(let,[status(thm),assumptions([e1_2__armstrng,dt_c1_2__armstrng])],[i3_2_tmp__armstrng,dh_c2_2__armstrng]),
    [interesting(0.8),file(armstrng,i2_2__armstrng),[file(armstrng,i2_2__armstrng)]]).

fof(i1_2__armstrng,plain,
    ( v2_finsub_1(c1_2__armstrng)
   => ! [A,B] : 
        ( ( v1_finset_1(B)
          & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
       => ( ( r2_hidden(A,c1_2__armstrng)
            & r1_tarski(B,c1_2__armstrng) )
         => r2_hidden(k8_setfam_1(A,B),c1_2__armstrng) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_2__armstrng]),discharge_asm(discharge,[e1_2__armstrng])],[e1_2__armstrng,i2_2__armstrng]),
    [interesting(0.8),file(armstrng,i1_2__armstrng),[file(armstrng,i1_2__armstrng)]]).

fof(i1_2_tmp__armstrng,plain,
    ( v2_finsub_1(c1_2__armstrng)
   => ! [A,B] : 
        ( ( v1_finset_1(B)
          & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
       => ( ( r2_hidden(A,c1_2__armstrng)
            & r1_tarski(B,c1_2__armstrng) )
         => r2_hidden(k8_setfam_1(A,B),c1_2__armstrng) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_2__armstrng])],[dt_c1_2__armstrng,i1_2__armstrng]),
    [interesting(1),t1_armstrng]).

fof(t1_armstrng,theorem,(
    ! [A] : 
      ( v2_finsub_1(A)
     => ! [B,C] : 
          ( ( v1_finset_1(C)
            & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(B))) )
         => ( ( r2_hidden(B,A)
              & r1_tarski(C,A) )
           => r2_hidden(k8_setfam_1(B,C),A) ) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_2_tmp__armstrng,dh_c1_2__armstrng]),
    [interesting(1),file(armstrng,t1_armstrng),[file(armstrng,t1_armstrng)]]).