% Mizar ND problem: t2_ami_7,ami_7,57,20 
fof(dh_c1_2__ami_7,definition,
    ( ( v1_setfam_1(c1_2__ami_7)
     => ! [A] : 
          ( ( ~ v3_struct_0(A)
            & ~ v2_ami_1(A,c1_2__ami_7)
            & l1_ami_1(A,c1_2__ami_7) )
         => ! [B] : 
              ( m1_subset_1(B,k4_card_3(u5_ami_1(c1_2__ami_7,A)))
             => ! [C] : 
                  ( m1_subset_1(C,u1_struct_0(A))
                 => r2_hidden(k1_funct_1(B,C),k3_ami_1(c1_2__ami_7,A,C)) ) ) ) )
   => ! [D] : 
        ( v1_setfam_1(D)
       => ! [E] : 
            ( ( ~ v3_struct_0(E)
              & ~ v2_ami_1(E,D)
              & l1_ami_1(E,D) )
           => ! [F] : 
                ( m1_subset_1(F,k4_card_3(u5_ami_1(D,E)))
               => ! [G] : 
                    ( m1_subset_1(G,u1_struct_0(E))
                   => r2_hidden(k1_funct_1(F,G),k3_ami_1(D,E,G)) ) ) ) ) ),
    introduced(definition,[new_symbol(c1_2__ami_7),file(ami_7,c1_2__ami_7)]),
    [interesting(0.8),axiom,file(ami_7,c1_2__ami_7)]).

fof(dh_c2_2__ami_7,definition,
    ( ( ( ~ v3_struct_0(c2_2__ami_7)
        & ~ v2_ami_1(c2_2__ami_7,c1_2__ami_7)
        & l1_ami_1(c2_2__ami_7,c1_2__ami_7) )
     => ! [A] : 
          ( m1_subset_1(A,k4_card_3(u5_ami_1(c1_2__ami_7,c2_2__ami_7)))
         => ! [B] : 
              ( m1_subset_1(B,u1_struct_0(c2_2__ami_7))
             => r2_hidden(k1_funct_1(A,B),k3_ami_1(c1_2__ami_7,c2_2__ami_7,B)) ) ) )
   => ! [C] : 
        ( ( ~ v3_struct_0(C)
          & ~ v2_ami_1(C,c1_2__ami_7)
          & l1_ami_1(C,c1_2__ami_7) )
       => ! [D] : 
            ( m1_subset_1(D,k4_card_3(u5_ami_1(c1_2__ami_7,C)))
           => ! [E] : 
                ( m1_subset_1(E,u1_struct_0(C))
               => r2_hidden(k1_funct_1(D,E),k3_ami_1(c1_2__ami_7,C,E)) ) ) ) ),
    introduced(definition,[new_symbol(c2_2__ami_7),file(ami_7,c2_2__ami_7)]),
    [interesting(0.8),axiom,file(ami_7,c2_2__ami_7)]).

fof(dh_c3_2__ami_7,definition,
    ( ( m1_subset_1(c3_2__ami_7,k4_card_3(u5_ami_1(c1_2__ami_7,c2_2__ami_7)))
     => ! [A] : 
          ( m1_subset_1(A,u1_struct_0(c2_2__ami_7))
         => r2_hidden(k1_funct_1(c3_2__ami_7,A),k3_ami_1(c1_2__ami_7,c2_2__ami_7,A)) ) )
   => ! [B] : 
        ( m1_subset_1(B,k4_card_3(u5_ami_1(c1_2__ami_7,c2_2__ami_7)))
       => ! [C] : 
            ( m1_subset_1(C,u1_struct_0(c2_2__ami_7))
           => r2_hidden(k1_funct_1(B,C),k3_ami_1(c1_2__ami_7,c2_2__ami_7,C)) ) ) ),
    introduced(definition,[new_symbol(c3_2__ami_7),file(ami_7,c3_2__ami_7)]),
    [interesting(0.8),axiom,file(ami_7,c3_2__ami_7)]).

fof(dh_c4_2__ami_7,definition,
    ( ( m1_subset_1(c4_2__ami_7,u1_struct_0(c2_2__ami_7))
     => r2_hidden(k1_funct_1(c3_2__ami_7,c4_2__ami_7),k3_ami_1(c1_2__ami_7,c2_2__ami_7,c4_2__ami_7)) )
   => ! [A] : 
        ( m1_subset_1(A,u1_struct_0(c2_2__ami_7))
       => r2_hidden(k1_funct_1(c3_2__ami_7,A),k3_ami_1(c1_2__ami_7,c2_2__ami_7,A)) ) ),
    introduced(definition,[new_symbol(c4_2__ami_7),file(ami_7,c4_2__ami_7)]),
    [interesting(0.8),axiom,file(ami_7,c4_2__ami_7)]).

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

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_k13_finseq_1,axiom,(
    $true ),
    file(finseq_1,k13_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,k13_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(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_k3_tarski,axiom,(
    $true ),
    file(tarski,k3_tarski),
    [interesting(0.9),axiom,file(tarski,k3_tarski)]).

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_u3_ami_1,axiom,(
    ! [A,B] : 
      ( l1_ami_1(B,A)
     => ~ v1_xboole_0(u3_ami_1(A,B)) ) ),
    file(ami_1,u3_ami_1),
    [interesting(0.9),axiom,file(ami_1,u3_ami_1)]).

fof(cc1_relset_1,theorem,(
    ! [A,B,C] : 
      ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
     => v1_relat_1(C) ) ),
    file(relset_1,cc1_relset_1),
    [interesting(0.9),axiom,file(relset_1,cc1_relset_1)]).

fof(fc1_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(fc4_ami_1,theorem,(
    ! [A,B,C] : 
      ( ( v1_setfam_1(B)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B) )
     => ( ~ v1_xboole_0(k4_card_3(C))
        & v1_fraenkel(k4_card_3(C)) ) ) ),
    file(ami_1,fc4_ami_1),
    [interesting(0.9),axiom,file(ami_1,fc4_ami_1)]).

fof(rc1_amistd_2,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_fraenkel(A)
      & v1_pralg_2(A)
      & v1_amistd_2(A) ) ),
    file(amistd_2,rc1_amistd_2),
    [interesting(0.9),axiom,file(amistd_2,rc1_amistd_2)]).

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(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(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(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(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(existence_l1_ami_1,axiom,(
    ! [A] : 
    ? [B] : l1_ami_1(B,A) ),
    file(ami_1,l1_ami_1),
    [interesting(0.9),axiom,file(ami_1,l1_ami_1)]).

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_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_k8_funct_2,definition,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B)
        & m1_subset_1(D,A) )
     => k8_funct_2(A,B,C,D) = k1_funct_1(C,D) ) ),
    file(funct_2,k8_funct_2),
    [interesting(0.9),axiom,file(funct_2,k8_funct_2)]).

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_k2_tarski,axiom,(
    $true ),
    file(tarski,k2_tarski),
    [interesting(0.9),axiom,file(tarski,k2_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(dt_k8_funct_2,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B)
        & m1_subset_1(D,A) )
     => m1_subset_1(k8_funct_2(A,B,C,D),B) ) ),
    file(funct_2,k8_funct_2),
    [interesting(0.9),axiom,file(funct_2,k8_funct_2)]).

fof(dt_l1_ami_1,axiom,(
    ! [A,B] : 
      ( l1_ami_1(B,A)
     => l1_struct_0(B) ) ),
    file(ami_1,l1_ami_1),
    [interesting(0.9),axiom,file(ami_1,l1_ami_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_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    [interesting(0.9),axiom,file(subset_1,m1_subset_1)]).

fof(dt_m2_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ),
    file(relset_1,m2_relset_1),
    [interesting(0.9),axiom,file(relset_1,m2_relset_1)]).

fof(dt_u2_ami_1,axiom,(
    ! [A,B] : 
      ( l1_ami_1(B,A)
     => m1_subset_1(u2_ami_1(A,B),k1_zfmisc_1(u1_struct_0(B))) ) ),
    file(ami_1,u2_ami_1),
    [interesting(0.9),axiom,file(ami_1,u2_ami_1)]).

fof(dt_u4_ami_1,axiom,(
    ! [A,B] : 
      ( l1_ami_1(B,A)
     => ( ~ v1_xboole_0(u4_ami_1(A,B))
        & m1_subset_1(u4_ami_1(A,B),k1_zfmisc_1(k2_zfmisc_1(u3_ami_1(A,B),k13_finseq_1(k2_xboole_0(k3_tarski(A),u1_struct_0(B)))))) ) ) ),
    file(ami_1,u4_ami_1),
    [interesting(0.9),axiom,file(ami_1,u4_ami_1)]).

fof(cc1_amistd_2,theorem,(
    ! [A] : 
      ( v1_amistd_2(A)
     => ( v1_fraenkel(A)
        & v1_pralg_2(A) ) ) ),
    file(amistd_2,cc1_amistd_2),
    [interesting(0.9),axiom,file(amistd_2,cc1_amistd_2)]).

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_setfam_1,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_setfam_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ~ v1_xboole_0(B) ) ) ),
    file(setfam_1,cc1_setfam_1),
    [interesting(0.9),axiom,file(setfam_1,cc1_setfam_1)]).

fof(fc11_ami_1,theorem,(
    ! [A,B,C] : 
      ( ( v1_setfam_1(A)
        & ~ v3_struct_0(B)
        & ~ v2_ami_1(B,A)
        & l1_ami_1(B,A)
        & m1_subset_1(C,u1_struct_0(B)) )
     => ~ v1_xboole_0(k3_ami_1(A,B,C)) ) ),
    file(ami_1,fc11_ami_1),
    [interesting(0.9),axiom,file(ami_1,fc11_ami_1)]).

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(fc2_ami_1,theorem,(
    ! [A,B] : 
      ( ( ~ v2_ami_1(B,A)
        & l1_ami_1(B,A) )
     => ~ v1_xboole_0(u2_ami_1(A,B)) ) ),
    file(ami_1,fc2_ami_1),
    [interesting(0.9),axiom,file(ami_1,fc2_ami_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_setfam_1,theorem,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ( ~ v1_xboole_0(k2_tarski(A,B))
        & v1_setfam_1(k2_tarski(A,B)) ) ) ),
    file(setfam_1,fc3_setfam_1),
    [interesting(0.9),axiom,file(setfam_1,fc3_setfam_1)]).

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(fc4_setfam_1,theorem,(
    ! [A,B] : 
      ( ( v1_setfam_1(A)
        & v1_setfam_1(B) )
     => v1_setfam_1(k2_xboole_0(A,B)) ) ),
    file(setfam_1,fc4_setfam_1),
    [interesting(0.9),axiom,file(setfam_1,fc4_setfam_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_setfam_1,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_setfam_1(A) ) ),
    file(setfam_1,rc1_setfam_1),
    [interesting(0.9),axiom,file(setfam_1,rc1_setfam_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_ami_1,theorem,(
    ! [A] : 
    ? [B] : 
      ( l1_ami_1(B,A)
      & ~ v3_struct_0(B)
      & ~ v2_ami_1(B,A) ) ),
    file(ami_1,rc2_ami_1),
    [interesting(0.9),axiom,file(ami_1,rc2_ami_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(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(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(dt_k1_funct_1,axiom,(
    $true ),
    file(funct_1,k1_funct_1),
    [interesting(0.9),axiom,file(funct_1,k1_funct_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_k3_ami_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(B)
        & l1_ami_1(B,A)
        & m1_subset_1(C,u1_struct_0(B)) )
     => m1_subset_1(k3_ami_1(A,B,C),k2_xboole_0(A,k2_tarski(u4_ami_1(A,B),u2_ami_1(A,B)))) ) ),
    file(ami_1,k3_ami_1),
    [interesting(0.9),axiom,file(ami_1,k3_ami_1)]).

fof(dt_k4_card_3,axiom,(
    $true ),
    file(card_3,k4_card_3),
    [interesting(0.9),axiom,file(card_3,k4_card_3)]).

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_u5_ami_1,axiom,(
    ! [A,B] : 
      ( l1_ami_1(B,A)
     => ( v1_funct_1(u5_ami_1(A,B))
        & v1_funct_2(u5_ami_1(A,B),u1_struct_0(B),k2_xboole_0(A,k2_tarski(u4_ami_1(A,B),u2_ami_1(A,B))))
        & m2_relset_1(u5_ami_1(A,B),u1_struct_0(B),k2_xboole_0(A,k2_tarski(u4_ami_1(A,B),u2_ami_1(A,B)))) ) ) ),
    file(ami_1,u5_ami_1),
    [interesting(0.9),axiom,file(ami_1,u5_ami_1)]).

fof(dt_c1_2__ami_7,assumption,(
    v1_setfam_1(c1_2__ami_7) ),
    introduced(assumption,[file(ami_7,c1_2__ami_7)]),
    [interesting(0.8),axiom,file(ami_7,c1_2__ami_7)]).

fof(dt_c2_2__ami_7,assumption,
    ( ~ v3_struct_0(c2_2__ami_7)
    & ~ v2_ami_1(c2_2__ami_7,c1_2__ami_7)
    & l1_ami_1(c2_2__ami_7,c1_2__ami_7) ),
    introduced(assumption,[file(ami_7,c2_2__ami_7)]),
    [interesting(0.8),axiom,file(ami_7,c2_2__ami_7)]).

fof(dt_c3_2__ami_7,assumption,(
    m1_subset_1(c3_2__ami_7,k4_card_3(u5_ami_1(c1_2__ami_7,c2_2__ami_7))) ),
    introduced(assumption,[file(ami_7,c3_2__ami_7)]),
    [interesting(0.8),axiom,file(ami_7,c3_2__ami_7)]).

fof(dt_c4_2__ami_7,assumption,(
    m1_subset_1(c4_2__ami_7,u1_struct_0(c2_2__ami_7)) ),
    introduced(assumption,[file(ami_7,c4_2__ami_7)]),
    [interesting(0.8),axiom,file(ami_7,c4_2__ami_7)]).

fof(cc1_amistd_1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( v1_relat_1(A)
        & v1_setfam_1(A) ) ) ),
    file(amistd_1,cc1_amistd_1),
    [interesting(0.9),axiom,file(amistd_1,cc1_amistd_1)]).

fof(fc3_ami_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => v1_fraenkel(k4_card_3(A)) ) ),
    file(ami_1,fc3_ami_1),
    [interesting(0.9),axiom,file(ami_1,fc3_ami_1)]).

fof(fc5_amistd_2,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_fraenkel(k4_card_3(A))
        & v1_amistd_2(k4_card_3(A)) ) ) ),
    file(amistd_2,fc5_amistd_2),
    [interesting(0.9),axiom,file(amistd_2,fc5_amistd_2)]).

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(d6_ami_1,definition,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(B)
        & l1_ami_1(B,A) )
     => ! [C] : 
          ( m1_subset_1(C,u1_struct_0(B))
         => k3_ami_1(A,B,C) = k8_funct_2(u1_struct_0(B),k2_xboole_0(A,k2_tarski(u4_ami_1(A,B),u2_ami_1(A,B))),u5_ami_1(A,B),C) ) ) ),
    file(ami_1,d6_ami_1),
    [interesting(0.9),axiom,file(ami_1,d6_ami_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_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(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(e1_2__ami_7,plain,(
    k1_relat_1(u5_ami_1(c1_2__ami_7,c2_2__ami_7)) = u1_struct_0(c2_2__ami_7) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2__ami_7,dt_c2_2__ami_7])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k13_finseq_1,dt_k3_tarski,dt_u3_ami_1,t1_subset,t4_subset,t5_subset,commutativity_k2_tarski,commutativity_k2_xboole_0,idempotence_k2_xboole_0,existence_l1_ami_1,existence_l1_struct_0,existence_m1_relset_1,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k2_tarski,dt_k2_xboole_0,dt_k2_zfmisc_1,dt_l1_ami_1,dt_l1_struct_0,dt_m1_relset_1,dt_m1_subset_1,dt_u2_ami_1,dt_u4_ami_1,cc1_amistd_1,cc1_relset_1,cc1_setfam_1,fc1_struct_0,fc2_ami_1,fc2_xboole_0,fc3_setfam_1,fc3_xboole_0,fc4_setfam_1,rc1_setfam_1,rc1_xboole_0,rc2_ami_1,rc2_xboole_0,rc3_struct_0,rc5_struct_0,t1_boole,t2_subset,t3_subset,t7_boole,t8_boole,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_u1_struct_0,dt_u5_ami_1,dt_c1_2__ami_7,dt_c2_2__ami_7,fc1_xboole_0,t6_boole,d1_funct_2]),
    [interesting(0.8),file(ami_7,e1_2__ami_7),[file(ami_7,e1_2__ami_7)]]).

fof(t18_card_3,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( r2_hidden(A,k4_card_3(B))
          <=> ( k1_relat_1(A) = k1_relat_1(B)
              & ! [C] : 
                  ( r2_hidden(C,k1_relat_1(B))
                 => r2_hidden(k1_funct_1(A,C),k1_funct_1(B,C)) ) ) ) ) ) ),
    file(card_3,t18_card_3),
    [interesting(0.9),axiom,file(card_3,t18_card_3)]).

fof(e2_2__ami_7,plain,(
    r2_hidden(k1_funct_1(c3_2__ami_7,c4_2__ami_7),k3_ami_1(c1_2__ami_7,c2_2__ami_7,c4_2__ami_7)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c3_2__ami_7,dt_c4_2__ami_7,dt_c1_2__ami_7,dt_c2_2__ami_7])],[reflexivity_r1_tarski,existence_m1_relset_1,dt_k13_finseq_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k3_tarski,dt_m1_relset_1,dt_u3_ami_1,cc1_relset_1,fc1_xboole_0,fc4_ami_1,rc1_amistd_2,rc5_struct_0,t1_boole,t3_subset,t4_subset,t5_subset,commutativity_k2_tarski,commutativity_k2_xboole_0,idempotence_k2_xboole_0,existence_l1_ami_1,existence_l1_struct_0,existence_m1_subset_1,existence_m2_relset_1,redefinition_k8_funct_2,redefinition_m2_relset_1,dt_k2_tarski,dt_k2_xboole_0,dt_k8_funct_2,dt_l1_ami_1,dt_l1_struct_0,dt_m1_subset_1,dt_m2_relset_1,dt_u2_ami_1,dt_u4_ami_1,cc1_amistd_2,cc1_fraenkel,cc1_setfam_1,fc11_ami_1,fc1_struct_0,fc2_ami_1,fc2_xboole_0,fc3_setfam_1,fc3_xboole_0,fc4_setfam_1,rc1_fraenkel,rc1_setfam_1,rc1_xboole_0,rc2_ami_1,rc2_xboole_0,rc3_struct_0,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k3_ami_1,dt_k4_card_3,dt_u1_struct_0,dt_u5_ami_1,dt_c1_2__ami_7,dt_c2_2__ami_7,dt_c3_2__ami_7,dt_c4_2__ami_7,cc1_amistd_1,fc3_ami_1,fc5_amistd_2,t1_subset,t7_boole,d6_ami_1,e1_2__ami_7,t18_card_3]),
    [interesting(0.8),file(ami_7,e2_2__ami_7),[file(ami_7,e2_2__ami_7)]]).

fof(i5_2__ami_7,theorem,(
    $true ),
    introduced(tautology,[file(ami_7,i5_2__ami_7)]),
    [interesting(0.8),trivial,file(ami_7,i5_2__ami_7)]).

fof(i4_2__ami_7,plain,(
    r2_hidden(k1_funct_1(c3_2__ami_7,c4_2__ami_7),k3_ami_1(c1_2__ami_7,c2_2__ami_7,c4_2__ami_7)) ),
    inference(conclusion,[status(thm),assumptions([dt_c3_2__ami_7,dt_c4_2__ami_7,dt_c1_2__ami_7,dt_c2_2__ami_7])],[e2_2__ami_7,i5_2__ami_7]),
    [interesting(0.8),file(ami_7,i4_2__ami_7),[file(ami_7,i4_2__ami_7)]]).

fof(i4_2_tmp__ami_7,plain,
    ( m1_subset_1(c4_2__ami_7,u1_struct_0(c2_2__ami_7))
   => r2_hidden(k1_funct_1(c3_2__ami_7,c4_2__ami_7),k3_ami_1(c1_2__ami_7,c2_2__ami_7,c4_2__ami_7)) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c3_2__ami_7,dt_c1_2__ami_7,dt_c2_2__ami_7]),discharge_asm(discharge,[dt_c4_2__ami_7])],[dt_c4_2__ami_7,i4_2__ami_7]),
    [interesting(0.8),i3_2__ami_7]).

fof(i3_2__ami_7,plain,(
    ! [A] : 
      ( m1_subset_1(A,u1_struct_0(c2_2__ami_7))
     => r2_hidden(k1_funct_1(c3_2__ami_7,A),k3_ami_1(c1_2__ami_7,c2_2__ami_7,A)) ) ),
    inference(let,[status(thm),assumptions([dt_c3_2__ami_7,dt_c1_2__ami_7,dt_c2_2__ami_7])],[i4_2_tmp__ami_7,dh_c4_2__ami_7]),
    [interesting(0.8),file(ami_7,i3_2__ami_7),[file(ami_7,i3_2__ami_7)]]).

fof(i3_2_tmp__ami_7,plain,
    ( m1_subset_1(c3_2__ami_7,k4_card_3(u5_ami_1(c1_2__ami_7,c2_2__ami_7)))
   => ! [A] : 
        ( m1_subset_1(A,u1_struct_0(c2_2__ami_7))
       => r2_hidden(k1_funct_1(c3_2__ami_7,A),k3_ami_1(c1_2__ami_7,c2_2__ami_7,A)) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_2__ami_7,dt_c2_2__ami_7]),discharge_asm(discharge,[dt_c3_2__ami_7])],[dt_c3_2__ami_7,i3_2__ami_7]),
    [interesting(0.8),i2_2__ami_7]).

fof(i2_2__ami_7,plain,(
    ! [A] : 
      ( m1_subset_1(A,k4_card_3(u5_ami_1(c1_2__ami_7,c2_2__ami_7)))
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(c2_2__ami_7))
         => r2_hidden(k1_funct_1(A,B),k3_ami_1(c1_2__ami_7,c2_2__ami_7,B)) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_2__ami_7,dt_c2_2__ami_7])],[i3_2_tmp__ami_7,dh_c3_2__ami_7]),
    [interesting(0.8),file(ami_7,i2_2__ami_7),[file(ami_7,i2_2__ami_7)]]).

fof(i2_2_tmp__ami_7,plain,
    ( ( ~ v3_struct_0(c2_2__ami_7)
      & ~ v2_ami_1(c2_2__ami_7,c1_2__ami_7)
      & l1_ami_1(c2_2__ami_7,c1_2__ami_7) )
   => ! [A] : 
        ( m1_subset_1(A,k4_card_3(u5_ami_1(c1_2__ami_7,c2_2__ami_7)))
       => ! [B] : 
            ( m1_subset_1(B,u1_struct_0(c2_2__ami_7))
           => r2_hidden(k1_funct_1(A,B),k3_ami_1(c1_2__ami_7,c2_2__ami_7,B)) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_2__ami_7]),discharge_asm(discharge,[dt_c2_2__ami_7])],[dt_c2_2__ami_7,i2_2__ami_7]),
    [interesting(0.8),i1_2__ami_7]).

fof(i1_2__ami_7,plain,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_ami_1(A,c1_2__ami_7)
        & l1_ami_1(A,c1_2__ami_7) )
     => ! [B] : 
          ( m1_subset_1(B,k4_card_3(u5_ami_1(c1_2__ami_7,A)))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => r2_hidden(k1_funct_1(B,C),k3_ami_1(c1_2__ami_7,A,C)) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_2__ami_7])],[i2_2_tmp__ami_7,dh_c2_2__ami_7]),
    [interesting(0.8),file(ami_7,i1_2__ami_7),[file(ami_7,i1_2__ami_7)]]).

fof(i1_2_tmp__ami_7,plain,
    ( v1_setfam_1(c1_2__ami_7)
   => ! [A] : 
        ( ( ~ v3_struct_0(A)
          & ~ v2_ami_1(A,c1_2__ami_7)
          & l1_ami_1(A,c1_2__ami_7) )
       => ! [B] : 
            ( m1_subset_1(B,k4_card_3(u5_ami_1(c1_2__ami_7,A)))
           => ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => r2_hidden(k1_funct_1(B,C),k3_ami_1(c1_2__ami_7,A,C)) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_2__ami_7])],[dt_c1_2__ami_7,i1_2__ami_7]),
    [interesting(1),t2_ami_7]).

fof(t2_ami_7,theorem,(
    ! [A] : 
      ( v1_setfam_1(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] : 
              ( m1_subset_1(C,k4_card_3(u5_ami_1(A,B)))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(B))
                 => r2_hidden(k1_funct_1(C,D),k3_ami_1(A,B,D)) ) ) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_2_tmp__ami_7,dh_c1_2__ami_7]),
    [interesting(1),file(ami_7,t2_ami_7),[file(ami_7,t2_ami_7)]]).