% Mizar problem: t7_algstr_3,algstr_3,158,22 
fof(t7_algstr_3,conjecture,(
    1 = k2_algstr_3(k4_algstr_3) ),
    inference(mizar_bg_added,[status(thm)],[reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k2_zfmisc_1,cc1_membered,cc2_membered,cc3_membered,rc1_membered,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc20_membered,t1_subset,t4_subset,t5_subset,existence_l1_struct_0,existence_l2_struct_0,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_zfmisc_1,dt_k3_zfmisc_1,dt_k5_ordinal2,dt_l1_struct_0,dt_l2_struct_0,dt_m1_relset_1,dt_m2_relset_1,dt_u2_algstr_3,dt_u2_struct_0,rc3_struct_0,rc4_struct_0,fc1_struct_0,rc5_struct_0,cc4_membered,cc6_membered,cc9_membered,fc5_membered,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,t2_subset,t3_subset,free_g1_algstr_3,abstractness_v1_algstr_3,existence_l1_algstr_3,existence_m1_subset_1,redefinition_k5_numbers,dt_g1_algstr_3,dt_k1_numbers,dt_k3_algstr_3,dt_k5_numbers,dt_l1_algstr_3,dt_m1_subset_1,dt_u1_algstr_3,dt_u1_struct_0,rc1_algstr_3,rc2_algstr_3,fc2_membered,t1_numerals,dt_k2_algstr_3,dt_k4_algstr_3,fc1_algstr_3,d3_algstr_3,d5_algstr_3,spc1_numerals]),
    [file(algstr_3,t7_algstr_3)]).

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

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

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

fof(cc1_membered,axiom,(
    ! [A] : 
      ( v5_membered(A)
     => v4_membered(A) ) ),
    file(membered,cc1_membered),
    []).

fof(cc2_membered,axiom,(
    ! [A] : 
      ( v4_membered(A)
     => v3_membered(A) ) ),
    file(membered,cc2_membered),
    []).

fof(cc3_membered,axiom,(
    ! [A] : 
      ( v3_membered(A)
     => v2_membered(A) ) ),
    file(membered,cc3_membered),
    []).

fof(rc1_membered,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_membered(A)
      & v2_membered(A)
      & v3_membered(A)
      & v4_membered(A)
      & v5_membered(A) ) ),
    file(membered,rc1_membered),
    []).

fof(cc12_membered,axiom,(
    ! [A] : 
      ( v3_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc12_membered),
    []).

fof(cc13_membered,axiom,(
    ! [A] : 
      ( v4_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B)
            & v1_int_1(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc13_membered),
    []).

fof(cc14_membered,axiom,(
    ! [A] : 
      ( v5_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v4_ordinal2(B)
            & v1_xreal_0(B)
            & v1_int_1(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc14_membered),
    []).

fof(cc18_membered,axiom,(
    ! [A] : 
      ( v3_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B) ) ) ) ),
    file(membered,cc18_membered),
    []).

fof(cc19_membered,axiom,(
    ! [A] : 
      ( v4_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B)
            & v4_membered(B) ) ) ) ),
    file(membered,cc19_membered),
    []).

fof(cc20_membered,axiom,(
    ! [A] : 
      ( v5_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B)
            & v4_membered(B)
            & v5_membered(B) ) ) ) ),
    file(membered,cc20_membered),
    []).

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

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

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

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

fof(existence_l2_struct_0,axiom,(
    ? [A] : l2_struct_0(A) ),
    file(struct_0,l2_struct_0),
    []).

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

fof(existence_m2_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m2_relset_1(C,A,B) ),
    file(relset_1,m2_relset_1),
    []).

fof(redefinition_m2_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
    <=> m1_relset_1(C,A,B) ) ),
    file(relset_1,m2_relset_1),
    []).

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

fof(dt_k3_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k3_zfmisc_1),
    []).

fof(dt_k5_ordinal2,axiom,(
    $true ),
    file(ordinal2,k5_ordinal2),
    []).

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

fof(dt_l2_struct_0,axiom,(
    ! [A] : 
      ( l2_struct_0(A)
     => l1_struct_0(A) ) ),
    file(struct_0,l2_struct_0),
    []).

fof(dt_m1_relset_1,axiom,(
    $true ),
    file(relset_1,m1_relset_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),
    []).

fof(dt_u2_algstr_3,axiom,(
    ! [A] : 
      ( l1_algstr_3(A)
     => ( v1_funct_1(u2_algstr_3(A))
        & v1_funct_2(u2_algstr_3(A),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
        & m2_relset_1(u2_algstr_3(A),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) ) ) ),
    file(algstr_3,u2_algstr_3),
    []).

fof(dt_u2_struct_0,axiom,(
    ! [A] : 
      ( l2_struct_0(A)
     => m1_subset_1(u2_struct_0(A),u1_struct_0(A)) ) ),
    file(struct_0,u2_struct_0),
    []).

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

fof(rc4_struct_0,axiom,(
    ? [A] : 
      ( l2_struct_0(A)
      & ~ v3_struct_0(A) ) ),
    file(struct_0,rc4_struct_0),
    []).

fof(fc1_struct_0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ~ v1_xboole_0(u1_struct_0(A)) ) ),
    file(struct_0,fc1_struct_0),
    []).

fof(rc5_struct_0,axiom,(
    ! [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),
    []).

fof(cc4_membered,axiom,(
    ! [A] : 
      ( v2_membered(A)
     => v1_membered(A) ) ),
    file(membered,cc4_membered),
    []).

fof(cc6_membered,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => ( v1_membered(A)
        & v2_membered(A) ) ) ),
    file(membered,cc6_membered),
    []).

fof(cc9_membered,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k5_numbers))
     => ( v1_membered(A)
        & v2_membered(A)
        & v3_membered(A)
        & v4_membered(A)
        & v5_membered(A) ) ) ),
    file(membered,cc9_membered),
    []).

fof(fc5_membered,axiom,
    ( v1_membered(k5_ordinal2)
    & v2_membered(k5_ordinal2)
    & v3_membered(k5_ordinal2)
    & v4_membered(k5_ordinal2)
    & v5_membered(k5_ordinal2) ),
    file(membered,fc5_membered),
    []).

fof(cc10_membered,axiom,(
    ! [A] : 
      ( v1_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => v1_xcmplx_0(B) ) ) ),
    file(membered,cc10_membered),
    []).

fof(cc11_membered,axiom,(
    ! [A] : 
      ( v2_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B) ) ) ) ),
    file(membered,cc11_membered),
    []).

fof(cc15_membered,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_membered(A)
        & v2_membered(A)
        & v3_membered(A)
        & v4_membered(A)
        & v5_membered(A) ) ) ),
    file(membered,cc15_membered),
    []).

fof(cc16_membered,axiom,(
    ! [A] : 
      ( v1_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => v1_membered(B) ) ) ),
    file(membered,cc16_membered),
    []).

fof(cc17_membered,axiom,(
    ! [A] : 
      ( v2_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B) ) ) ) ),
    file(membered,cc17_membered),
    []).

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

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

fof(free_g1_algstr_3,axiom,(
    ! [A,B,C,D] : 
      ( ( m1_subset_1(B,A)
        & m1_subset_1(C,A)
        & v1_funct_1(D)
        & v1_funct_2(D,k3_zfmisc_1(A,A,A),A)
        & m1_relset_1(D,k3_zfmisc_1(A,A,A),A) )
     => ! [E,F,G,H] : 
          ( g1_algstr_3(A,B,C,D) = g1_algstr_3(E,F,G,H)
         => ( A = E
            & B = F
            & C = G
            & D = H ) ) ) ),
    file(algstr_3,g1_algstr_3),
    []).

fof(abstractness_v1_algstr_3,axiom,(
    ! [A] : 
      ( l1_algstr_3(A)
     => ( v1_algstr_3(A)
       => A = g1_algstr_3(u1_struct_0(A),u2_struct_0(A),u1_algstr_3(A),u2_algstr_3(A)) ) ) ),
    file(algstr_3,v1_algstr_3),
    []).

fof(existence_l1_algstr_3,axiom,(
    ? [A] : l1_algstr_3(A) ),
    file(algstr_3,l1_algstr_3),
    []).

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

fof(redefinition_k5_numbers,axiom,(
    k5_numbers = k5_ordinal2 ),
    file(numbers,k5_numbers),
    []).

fof(dt_g1_algstr_3,axiom,(
    ! [A,B,C,D] : 
      ( ( m1_subset_1(B,A)
        & m1_subset_1(C,A)
        & v1_funct_1(D)
        & v1_funct_2(D,k3_zfmisc_1(A,A,A),A)
        & m1_relset_1(D,k3_zfmisc_1(A,A,A),A) )
     => ( v1_algstr_3(g1_algstr_3(A,B,C,D))
        & l1_algstr_3(g1_algstr_3(A,B,C,D)) ) ) ),
    file(algstr_3,g1_algstr_3),
    []).

fof(dt_k1_numbers,axiom,(
    $true ),
    file(numbers,k1_numbers),
    []).

fof(dt_k3_algstr_3,axiom,
    ( v1_funct_1(k3_algstr_3)
    & v1_funct_2(k3_algstr_3,k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers),k1_numbers)
    & m2_relset_1(k3_algstr_3,k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers),k1_numbers) ),
    file(algstr_3,k3_algstr_3),
    []).

fof(dt_k5_numbers,axiom,(
    m1_subset_1(k5_numbers,k1_zfmisc_1(k1_numbers)) ),
    file(numbers,k5_numbers),
    []).

fof(dt_l1_algstr_3,axiom,(
    ! [A] : 
      ( l1_algstr_3(A)
     => l2_struct_0(A) ) ),
    file(algstr_3,l1_algstr_3),
    []).

fof(dt_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    []).

fof(dt_u1_algstr_3,axiom,(
    ! [A] : 
      ( l1_algstr_3(A)
     => m1_subset_1(u1_algstr_3(A),u1_struct_0(A)) ) ),
    file(algstr_3,u1_algstr_3),
    []).

fof(dt_u1_struct_0,axiom,(
    $true ),
    file(struct_0,u1_struct_0),
    []).

fof(rc1_algstr_3,axiom,(
    ? [A] : 
      ( l1_algstr_3(A)
      & v1_algstr_3(A) ) ),
    file(algstr_3,rc1_algstr_3),
    []).

fof(rc2_algstr_3,axiom,(
    ? [A] : 
      ( l1_algstr_3(A)
      & ~ v3_struct_0(A) ) ),
    file(algstr_3,rc2_algstr_3),
    []).

fof(fc2_membered,axiom,
    ( ~ v1_xboole_0(k1_numbers)
    & v1_membered(k1_numbers)
    & v2_membered(k1_numbers) ),
    file(membered,fc2_membered),
    []).

fof(t1_numerals,axiom,(
    m1_subset_1(0,k5_numbers) ),
    file(numerals,t1_numerals),
    []).

fof(dt_k2_algstr_3,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_algstr_3(A) )
     => m1_subset_1(k2_algstr_3(A),u1_struct_0(A)) ) ),
    file(algstr_3,k2_algstr_3),
    []).

fof(dt_k4_algstr_3,axiom,
    ( v1_algstr_3(k4_algstr_3)
    & l1_algstr_3(k4_algstr_3) ),
    file(algstr_3,k4_algstr_3),
    []).

fof(fc1_algstr_3,axiom,
    ( ~ v3_struct_0(k4_algstr_3)
    & v1_algstr_3(k4_algstr_3) ),
    file(algstr_3,fc1_algstr_3),
    []).

fof(d3_algstr_3,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_algstr_3(A) )
     => k2_algstr_3(A) = u1_algstr_3(A) ) ),
    file(algstr_3,d3_algstr_3),
    []).

fof(d5_algstr_3,axiom,(
    k4_algstr_3 = g1_algstr_3(k1_numbers,0,1,k3_algstr_3) ),
    file(algstr_3,d5_algstr_3),
    []).

fof(spc1_numerals,axiom,
    ( v2_xreal_0(1)
    & m1_subset_1(1,k5_numbers) ),
    file(numerals,spc1_numerals),
    []).